Determine The Surface Area Of A Rectangular Prism With The Following Dimensions:Length = 4 Cm 4 \, \text{cm} 4 Cm , Width = 2 Cm 2 \, \text{cm} 2 Cm , Height = 3 Cm 3 \, \text{cm} 3 Cm .a. 52 Sq. cm 52 \, \text{sq. Cm} 52 Sq. cm B. $104 , \text{sq.

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Introduction

In geometry, a rectangular prism is a three-dimensional shape with six rectangular faces. The surface area of a rectangular prism is the total area of its six faces. In this article, we will determine the surface area of a rectangular prism with the given dimensions: Length = 4 cm4 \, \text{cm}, Width = 2 cm2 \, \text{cm}, and Height = 3 cm3 \, \text{cm}.

Understanding the Formula

The surface area of a rectangular prism can be calculated using the formula:

SA=2lw+2lh+2whSA = 2lw + 2lh + 2wh

where SASA is the surface area, ll is the length, ww is the width, and hh is the height.

Calculating the Surface Area

To calculate the surface area of the given rectangular prism, we will substitute the given values into the formula:

SA=2(4)(2)+2(4)(3)+2(2)(3)SA = 2(4)(2) + 2(4)(3) + 2(2)(3)

SA=16+24+12SA = 16 + 24 + 12

SA=52 sq. cmSA = 52 \, \text{sq. cm}

Verification

To verify the result, we can calculate the surface area of the rectangular prism using a different method. We can calculate the area of each face and add them together:

  • Area of the front face: lw=(4)(2)=8 sq. cmlw = (4)(2) = 8 \, \text{sq. cm}
  • Area of the back face: lw=(4)(2)=8 sq. cmlw = (4)(2) = 8 \, \text{sq. cm}
  • Area of the top face: wh=(2)(3)=6 sq. cmwh = (2)(3) = 6 \, \text{sq. cm}
  • Area of the bottom face: wh=(2)(3)=6 sq. cmwh = (2)(3) = 6 \, \text{sq. cm}
  • Area of the left face: lh=(4)(3)=12 sq. cmlh = (4)(3) = 12 \, \text{sq. cm}
  • Area of the right face: lh=(4)(3)=12 sq. cmlh = (4)(3) = 12 \, \text{sq. cm}

Adding the areas of all the faces together, we get:

SA=8+8+6+6+12+12SA = 8 + 8 + 6 + 6 + 12 + 12

SA=52 sq. cmSA = 52 \, \text{sq. cm}

Conclusion

In this article, we determined the surface area of a rectangular prism with the given dimensions: Length = 4 cm4 \, \text{cm}, Width = 2 cm2 \, \text{cm}, and Height = 3 cm3 \, \text{cm}. We used the formula SA=2lw+2lh+2whSA = 2lw + 2lh + 2wh to calculate the surface area, which resulted in 52 sq. cm52 \, \text{sq. cm}. We also verified the result by calculating the area of each face and adding them together.

Surface Area of Rectangular Prism Formula

The surface area of a rectangular prism can be calculated using the formula:

SA=2lw+2lh+2whSA = 2lw + 2lh + 2wh

where SASA is the surface area, ll is the length, ww is the width, and hh is the height.

Rectangular Prism Surface Area Example

To calculate the surface area of a rectangular prism with the given dimensions: Length = 4 cm4 \, \text{cm}, Width = 2 cm2 \, \text{cm}, and Height = 3 cm3 \, \text{cm}, we can use the formula:

SA=2(4)(2)+2(4)(3)+2(2)(3)SA = 2(4)(2) + 2(4)(3) + 2(2)(3)

SA=16+24+12SA = 16 + 24 + 12

SA=52 sq. cmSA = 52 \, \text{sq. cm}

Rectangular Prism Surface Area Calculation

To calculate the surface area of a rectangular prism, we can use the formula:

SA=2lw+2lh+2whSA = 2lw + 2lh + 2wh

where SASA is the surface area, ll is the length, ww is the width, and hh is the height.

Rectangular Prism Surface Area Formula Derivation

The surface area of a rectangular prism can be calculated by adding the areas of all its faces. The formula for the surface area of a rectangular prism is:

SA=2lw+2lh+2whSA = 2lw + 2lh + 2wh

where SASA is the surface area, ll is the length, ww is the width, and hh is the height.

Rectangular Prism Surface Area Example Solution

To calculate the surface area of a rectangular prism with the given dimensions: Length = 4 cm4 \, \text{cm}, Width = 2 cm2 \, \text{cm}, and Height = 3 cm3 \, \text{cm}, we can use the formula:

SA=2(4)(2)+2(4)(3)+2(2)(3)SA = 2(4)(2) + 2(4)(3) + 2(2)(3)

SA=16+24+12SA = 16 + 24 + 12

SA=52 sq. cmSA = 52 \, \text{sq. cm}

Rectangular Prism Surface Area Formula Proof

The surface area of a rectangular prism can be calculated by adding the areas of all its faces. The formula for the surface area of a rectangular prism is:

SA=2lw+2lh+2whSA = 2lw + 2lh + 2wh

where SASA is the surface area, ll is the length, ww is the width, and hh is the height.

Rectangular Prism Surface Area Calculation Steps

To calculate the surface area of a rectangular prism, we can follow these steps:

  1. Calculate the area of the front face: lwlw
  2. Calculate the area of the back face: lwlw
  3. Calculate the area of the top face: whwh
  4. Calculate the area of the bottom face: whwh
  5. Calculate the area of the left face: lhlh
  6. Calculate the area of the right face: lhlh
  7. Add the areas of all the faces together: SA=lw+lw+wh+wh+lh+lhSA = lw + lw + wh + wh + lh + lh

Rectangular Prism Surface Area Formula Simplification

The surface area of a rectangular prism can be calculated using the formula:

SA=2lw+2lh+2whSA = 2lw + 2lh + 2wh

where SASA is the surface area, ll is the length, ww is the width, and hh is the height.

Rectangular Prism Surface Area Example Simplification

To calculate the surface area of a rectangular prism with the given dimensions: Length = 4 cm4 \, \text{cm}, Width = 2 cm2 \, \text{cm}, and Height = 3 cm3 \, \text{cm}, we can use the formula:

SA=2(4)(2)+2(4)(3)+2(2)(3)SA = 2(4)(2) + 2(4)(3) + 2(2)(3)

SA=16+24+12SA = 16 + 24 + 12

SA=52 sq. cmSA = 52 \, \text{sq. cm}

Rectangular Prism Surface Area Formula Extension

The surface area of a rectangular prism can be calculated using the formula:

SA=2lw+2lh+2whSA = 2lw + 2lh + 2wh

where SASA is the surface area, ll is the length, ww is the width, and hh is the height.

Rectangular Prism Surface Area Example Extension

To calculate the surface area of a rectangular prism with the given dimensions: Length = 4 cm4 \, \text{cm}, Width = 2 cm2 \, \text{cm}, and Height = 3 cm3 \, \text{cm}, we can use the formula:

SA=2(4)(2)+2(4)(3)+2(2)(3)SA = 2(4)(2) + 2(4)(3) + 2(2)(3)

SA=16+24+12SA = 16 + 24 + 12

SA = 52 \, \text{sq. cm}$<br/> **Frequently Asked Questions (FAQs) About Rectangular Prism Surface Area** ====================================================================

Q: What is the surface area of a rectangular prism?

A: The surface area of a rectangular prism is the total area of its six faces.

Q: How do I calculate the surface area of a rectangular prism?

A: To calculate the surface area of a rectangular prism, you can use the formula:

SA=2lw+2lh+2wh</span></p><p>where<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi>A</mi></mrow><annotationencoding="application/x−tex">SA</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6833em;"></span><spanclass="mordmathnormal"style="margin−right:0.05764em;">S</span><spanclass="mordmathnormal">A</span></span></span></span>isthesurfacearea,<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi></mrow><annotationencoding="application/x−tex">l</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6944em;"></span><spanclass="mordmathnormal"style="margin−right:0.01968em;">l</span></span></span></span>isthelength,<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi></mrow><annotationencoding="application/x−tex">w</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.4306em;"></span><spanclass="mordmathnormal"style="margin−right:0.02691em;">w</span></span></span></span>isthewidth,and<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotationencoding="application/x−tex">h</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6944em;"></span><spanclass="mordmathnormal">h</span></span></span></span>istheheight.</p><h2><strong>Q:Whatarethedimensionsofarectangularprism?</strong></h2><p>A:Arectangularprismhasthreedimensions:length,width,andheight.</p><h2><strong>Q:HowdoIcalculatetheareaofeachfaceofarectangularprism?</strong></h2><p>A:Tocalculatetheareaofeachfaceofarectangularprism,youcanusetheformula:</p><ul><li>Areaofthefrontface:<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>w</mi></mrow><annotationencoding="application/x−tex">lw</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6944em;"></span><spanclass="mordmathnormal"style="margin−right:0.02691em;">lw</span></span></span></span></li><li>Areaofthebackface:<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>w</mi></mrow><annotationencoding="application/x−tex">lw</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6944em;"></span><spanclass="mordmathnormal"style="margin−right:0.02691em;">lw</span></span></span></span></li><li>Areaofthetopface:<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mi>h</mi></mrow><annotationencoding="application/x−tex">wh</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6944em;"></span><spanclass="mordmathnormal"style="margin−right:0.02691em;">w</span><spanclass="mordmathnormal">h</span></span></span></span></li><li>Areaofthebottomface:<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mi>h</mi></mrow><annotationencoding="application/x−tex">wh</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6944em;"></span><spanclass="mordmathnormal"style="margin−right:0.02691em;">w</span><spanclass="mordmathnormal">h</span></span></span></span></li><li>Areaoftheleftface:<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>h</mi></mrow><annotationencoding="application/x−tex">lh</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6944em;"></span><spanclass="mordmathnormal"style="margin−right:0.01968em;">l</span><spanclass="mordmathnormal">h</span></span></span></span></li><li>Areaoftherightface:<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>h</mi></mrow><annotationencoding="application/x−tex">lh</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6944em;"></span><spanclass="mordmathnormal"style="margin−right:0.01968em;">l</span><spanclass="mordmathnormal">h</span></span></span></span></li></ul><h2><strong>Q:HowdoIaddtheareasofallthefacestogethertocalculatethesurfaceareaofarectangularprism?</strong></h2><p>A:Toaddtheareasofallthefacestogether,youcanusetheformula:</p><pclass=′katex−block′><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mi>l</mi><mi>w</mi><mo>+</mo><mi>l</mi><mi>w</mi><mo>+</mo><mi>w</mi><mi>h</mi><mo>+</mo><mi>w</mi><mi>h</mi><mo>+</mo><mi>l</mi><mi>h</mi><mo>+</mo><mi>l</mi><mi>h</mi></mrow><annotationencoding="application/x−tex">SA=lw+lw+wh+wh+lh+lh</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6833em;"></span><spanclass="mordmathnormal"style="margin−right:0.05764em;">S</span><spanclass="mordmathnormal">A</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7778em;vertical−align:−0.0833em;"></span><spanclass="mordmathnormal"style="margin−right:0.02691em;">lw</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7778em;vertical−align:−0.0833em;"></span><spanclass="mordmathnormal"style="margin−right:0.02691em;">lw</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7778em;vertical−align:−0.0833em;"></span><spanclass="mordmathnormal"style="margin−right:0.02691em;">w</span><spanclass="mordmathnormal">h</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7778em;vertical−align:−0.0833em;"></span><spanclass="mordmathnormal"style="margin−right:0.02691em;">w</span><spanclass="mordmathnormal">h</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7778em;vertical−align:−0.0833em;"></span><spanclass="mordmathnormal"style="margin−right:0.01968em;">l</span><spanclass="mordmathnormal">h</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6944em;"></span><spanclass="mordmathnormal"style="margin−right:0.01968em;">l</span><spanclass="mordmathnormal">h</span></span></span></span></span></p><h2><strong>Q:CanIuseadifferentmethodtocalculatethesurfaceareaofarectangularprism?</strong></h2><p>A:Yes,youcanuseadifferentmethodtocalculatethesurfaceareaofarectangularprism.Forexample,youcancalculatetheareaofeachfaceandaddthemtogether.</p><h2><strong>Q:Whatistheformulaforthesurfaceareaofarectangularprismintermsofthedimensions?</strong></h2><p>A:Theformulaforthesurfaceareaofarectangularprismintermsofthedimensionsis:</p><pclass=′katex−block′><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>2</mn><mi>l</mi><mi>w</mi><mo>+</mo><mn>2</mn><mi>l</mi><mi>h</mi><mo>+</mo><mn>2</mn><mi>w</mi><mi>h</mi></mrow><annotationencoding="application/x−tex">SA=2lw+2lh+2wh</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6833em;"></span><spanclass="mordmathnormal"style="margin−right:0.05764em;">S</span><spanclass="mordmathnormal">A</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7778em;vertical−align:−0.0833em;"></span><spanclass="mord">2</span><spanclass="mordmathnormal"style="margin−right:0.02691em;">lw</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7778em;vertical−align:−0.0833em;"></span><spanclass="mord">2</span><spanclass="mordmathnormal"style="margin−right:0.01968em;">l</span><spanclass="mordmathnormal">h</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6944em;"></span><spanclass="mord">2</span><spanclass="mordmathnormal"style="margin−right:0.02691em;">w</span><spanclass="mordmathnormal">h</span></span></span></span></span></p><h2><strong>Q:CanIusetheformulatocalculatethesurfaceareaofarectangularprismwithdifferentdimensions?</strong></h2><p>A:Yes,youcanusetheformulatocalculatethesurfaceareaofarectangularprismwithdifferentdimensions.</p><h2><strong>Q:Whatisthesurfaceareaofarectangularprismwiththefollowingdimensions:Length=<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotationencoding="application/x−tex">4 cm</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">4</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">cm</span></span></span></span></span>,Width=<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotationencoding="application/x−tex">2 cm</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">2</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">cm</span></span></span></span></span>,andHeight=<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotationencoding="application/x−tex">3 cm</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">3</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">cm</span></span></span></span></span>?</strong></h2><p>A:Tocalculatethesurfaceareaofarectangularprismwiththegivendimensions,youcanusetheformula:</p><pclass=′katex−block′><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>2</mn><mostretchy="false">(</mo><mn>4</mn><mostretchy="false">)</mo><mostretchy="false">(</mo><mn>2</mn><mostretchy="false">)</mo><mo>+</mo><mn>2</mn><mostretchy="false">(</mo><mn>4</mn><mostretchy="false">)</mo><mostretchy="false">(</mo><mn>3</mn><mostretchy="false">)</mo><mo>+</mo><mn>2</mn><mostretchy="false">(</mo><mn>2</mn><mostretchy="false">)</mo><mostretchy="false">(</mo><mn>3</mn><mostretchy="false">)</mo></mrow><annotationencoding="application/x−tex">SA=2(4)(2)+2(4)(3)+2(2)(3)</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6833em;"></span><spanclass="mordmathnormal"style="margin−right:0.05764em;">S</span><spanclass="mordmathnormal">A</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">2</span><spanclass="mopen">(</span><spanclass="mord">4</span><spanclass="mclose">)</span><spanclass="mopen">(</span><spanclass="mord">2</span><spanclass="mclose">)</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">2</span><spanclass="mopen">(</span><spanclass="mord">4</span><spanclass="mclose">)</span><spanclass="mopen">(</span><spanclass="mord">3</span><spanclass="mclose">)</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">2</span><spanclass="mopen">(</span><spanclass="mord">2</span><spanclass="mclose">)</span><spanclass="mopen">(</span><spanclass="mord">3</span><spanclass="mclose">)</span></span></span></span></span></p><pclass=′katex−block′><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>16</mn><mo>+</mo><mn>24</mn><mo>+</mo><mn>12</mn></mrow><annotationencoding="application/x−tex">SA=16+24+12</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6833em;"></span><spanclass="mordmathnormal"style="margin−right:0.05764em;">S</span><spanclass="mordmathnormal">A</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">16</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">24</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">12</span></span></span></span></span></p><pclass=′katex−block′><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>52</mn><mtext> </mtext><mtext>sq. cm</mtext></mrow><annotationencoding="application/x−tex">SA=52 sq. cm</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6833em;"></span><spanclass="mordmathnormal"style="margin−right:0.05764em;">S</span><spanclass="mordmathnormal">A</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.8389em;vertical−align:−0.1944em;"></span><spanclass="mord">52</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">sq. cm</span></span></span></span></span></span></p><h2><strong>Q:CanIusetheformulatocalculatethesurfaceareaofarectangularprismwithdifferentunitsofmeasurement?</strong></h2><p>A:Yes,youcanusetheformulatocalculatethesurfaceareaofarectangularprismwithdifferentunitsofmeasurement.</p><h2><strong>Q:Whatisthesurfaceareaofarectangularprismwiththefollowingdimensions:Length=<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn><mtext> </mtext><mtext>in</mtext></mrow><annotationencoding="application/x−tex">5 in</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6679em;"></span><spanclass="mord">5</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">in</span></span></span></span></span>,Width=<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mtext> </mtext><mtext>in</mtext></mrow><annotationencoding="application/x−tex">3 in</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6679em;"></span><spanclass="mord">3</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">in</span></span></span></span></span>,andHeight=<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mtext>in</mtext></mrow><annotationencoding="application/x−tex">2 in</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6679em;"></span><spanclass="mord">2</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">in</span></span></span></span></span>?</strong></h2><p>A:Tocalculatethesurfaceareaofarectangularprismwiththegivendimensions,youcanusetheformula:</p><pclass=′katex−block′><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>2</mn><mostretchy="false">(</mo><mn>5</mn><mostretchy="false">)</mo><mostretchy="false">(</mo><mn>3</mn><mostretchy="false">)</mo><mo>+</mo><mn>2</mn><mostretchy="false">(</mo><mn>5</mn><mostretchy="false">)</mo><mostretchy="false">(</mo><mn>2</mn><mostretchy="false">)</mo><mo>+</mo><mn>2</mn><mostretchy="false">(</mo><mn>3</mn><mostretchy="false">)</mo><mostretchy="false">(</mo><mn>2</mn><mostretchy="false">)</mo></mrow><annotationencoding="application/x−tex">SA=2(5)(3)+2(5)(2)+2(3)(2)</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6833em;"></span><spanclass="mordmathnormal"style="margin−right:0.05764em;">S</span><spanclass="mordmathnormal">A</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">2</span><spanclass="mopen">(</span><spanclass="mord">5</span><spanclass="mclose">)</span><spanclass="mopen">(</span><spanclass="mord">3</span><spanclass="mclose">)</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">2</span><spanclass="mopen">(</span><spanclass="mord">5</span><spanclass="mclose">)</span><spanclass="mopen">(</span><spanclass="mord">2</span><spanclass="mclose">)</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">2</span><spanclass="mopen">(</span><spanclass="mord">3</span><spanclass="mclose">)</span><spanclass="mopen">(</span><spanclass="mord">2</span><spanclass="mclose">)</span></span></span></span></span></p><pclass=′katex−block′><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>30</mn><mo>+</mo><mn>20</mn><mo>+</mo><mn>12</mn></mrow><annotationencoding="application/x−tex">SA=30+20+12</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6833em;"></span><spanclass="mordmathnormal"style="margin−right:0.05764em;">S</span><spanclass="mordmathnormal">A</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">30</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">20</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">12</span></span></span></span></span></p><pclass=′katex−block′><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>62</mn><mtext> </mtext><mtext>sq. in</mtext></mrow><annotationencoding="application/x−tex">SA=62 sq. in</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6833em;"></span><spanclass="mordmathnormal"style="margin−right:0.05764em;">S</span><spanclass="mordmathnormal">A</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.8623em;vertical−align:−0.1944em;"></span><spanclass="mord">62</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">sq. in</span></span></span></span></span></span></p><h2><strong>Q:CanIusetheformulatocalculatethesurfaceareaofarectangularprismwithnegativedimensions?</strong></h2><p>A:No,youcannotusetheformulatocalculatethesurfaceareaofarectangularprismwithnegativedimensions.</p><h2><strong>Q:Whatisthesurfaceareaofarectangularprismwiththefollowingdimensions:Length=<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>4</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotationencoding="application/x−tex">−4 cm</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">−</span><spanclass="mord">4</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">cm</span></span></span></span></span>,Width=<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>2</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotationencoding="application/x−tex">−2 cm</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">−</span><spanclass="mord">2</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">cm</span></span></span></span></span>,andHeight=<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>3</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotationencoding="application/x−tex">−3 cm</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">−</span><spanclass="mord">3</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">cm</span></span></span></span></span>?</strong></h2><p>A:Sincethedimensionsarenegative,thesurfaceareaisnotdefined.</p><h2><strong>Q:CanIusetheformulatocalculatethesurfaceareaofarectangularprismwithfractionaldimensions?</strong></h2><p>A:Yes,youcanusetheformulatocalculatethesurfaceareaofarectangularprismwithfractionaldimensions.</p><h2><strong>Q:Whatisthesurfaceareaofarectangularprismwiththefollowingdimensions:Length=<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4.5</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotationencoding="application/x−tex">4.5 cm</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">4.5</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">cm</span></span></span></span></span>,Width=<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2.5</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotationencoding="application/x−tex">2.5 cm</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">2.5</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">cm</span></span></span></span></span>,andHeight=<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3.5</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotationencoding="application/x−tex">3.5 cm</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">3.5</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">cm</span></span></span></span></span>?</strong></h2><p>A:Tocalculatethesurfaceareaofarectangularprismwiththegivendimensions,youcanusetheformula:</p><pclass=′katex−block′><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>2</mn><mostretchy="false">(</mo><mn>4.5</mn><mostretchy="false">)</mo><mostretchy="false">(</mo><mn>2.5</mn><mostretchy="false">)</mo><mo>+</mo><mn>2</mn><mostretchy="false">(</mo><mn>4.5</mn><mostretchy="false">)</mo><mostretchy="false">(</mo><mn>3.5</mn><mostretchy="false">)</mo><mo>+</mo><mn>2</mn><mostretchy="false">(</mo><mn>2.5</mn><mostretchy="false">)</mo><mostretchy="false">(</mo><mn>3.5</mn><mostretchy="false">)</mo></mrow><annotationencoding="application/x−tex">SA=2(4.5)(2.5)+2(4.5)(3.5)+2(2.5)(3.5)</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6833em;"></span><spanclass="mordmathnormal"style="margin−right:0.05764em;">S</span><spanclass="mordmathnormal">A</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">2</span><spanclass="mopen">(</span><spanclass="mord">4.5</span><spanclass="mclose">)</span><spanclass="mopen">(</span><spanclass="mord">2.5</span><spanclass="mclose">)</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">2</span><spanclass="mopen">(</span><spanclass="mord">4.5</span><spanclass="mclose">)</span><spanclass="mopen">(</span><spanclass="mord">3.5</span><spanclass="mclose">)</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">2</span><spanclass="mopen">(</span><spanclass="mord">2.5</span><spanclass="mclose">)</span><spanclass="mopen">(</span><spanclass="mord">3.5</span><spanclass="mclose">)</span></span></span></span></span></p><pclass=′katex−block′><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>22.5</mn><mo>+</mo><mn>31.5</mn><mo>+</mo><mn>17.5</mn></mrow><annotationencoding="application/x−tex">SA=22.5+31.5+17.5</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6833em;"></span><spanclass="mordmathnormal"style="margin−right:0.05764em;">S</span><spanclass="mordmathnormal">A</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">22.5</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">31.5</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">17.5</span></span></span></span></span></p><pclass=′katex−block′><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>71.5</mn><mtext> </mtext><mtext>sq. cm</mtext></mrow><annotationencoding="application/x−tex">SA=71.5 sq. cm</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6833em;"></span><spanclass="mordmathnormal"style="margin−right:0.05764em;">S</span><spanclass="mordmathnormal">A</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.8389em;vertical−align:−0.1944em;"></span><spanclass="mord">71.5</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">sq. cm</span></span></span></span></span></span></p><h2><strong>Q:CanIusetheformulatocalculatethesurfaceareaofarectangularprismwithdecimaldimensions?</strong></h2><p>A:Yes,youcanusetheformulatocalculatethesurfaceareaofarectangularprismwithdecimaldimensions.</p><h2><strong>Q:Whatisthesurfaceareaofarectangularprismwiththefollowingdimensions:Length=<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4.2</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotationencoding="application/x−tex">4.2 cm</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">4.2</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">cm</span></span></span></span></span>,Width=<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2.1</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotationencoding="application/x−tex">2.1 cm</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">2.1</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">cm</span></span></span></span></span>,andHeight=<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3.3</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotationencoding="application/x−tex">3.3 cm</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">3.3</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">cm</span></span></span></span></span>?</strong></h2><p>A:Tocalculatethesurfaceareaofarectangularprismwiththegivendimensions,youcanusetheformula:</p><pclass=′katex−block′><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>2</mn><mostretchy="false">(</mo><mn>4.2</mn><mostretchy="false">)</mo><mostretchy="false">(</mo><mn>2.1</mn><mostretchy="false">)</mo><mo>+</mo><mn>2</mn><mostretchy="false">(</mo><mn>4.2</mn><mostretchy="false">)</mo><mostretchy="false">(</mo><mn>3.3</mn><mostretchy="false">)</mo><mo>+</mo><mn>2</mn><mostretchy="false">(</mo><mn>2.1</mn><mostretchy="false">)</mo><mostretchy="false">(</mo><mn>3.3</mn><mostretchy="false">)</mo></mrow><annotationencoding="application/x−tex">SA=2(4.2)(2.1)+2(4.2)(3.3)+2(2.1)(3.3)</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6833em;"></span><spanclass="mordmathnormal"style="margin−right:0.05764em;">S</span><spanclass="mordmathnormal">A</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">2</span><spanclass="mopen">(</span><spanclass="mord">4.2</span><spanclass="mclose">)</span><spanclass="mopen">(</span><spanclass="mord">2.1</span><spanclass="mclose">)</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">2</span><spanclass="mopen">(</span><spanclass="mord">4.2</span><spanclass="mclose">)</span><spanclass="mopen">(</span><spanclass="mord">3.3</span><spanclass="mclose">)</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">2</span><spanclass="mopen">(</span><spanclass="mord">2.1</span><spanclass="mclose">)</span><spanclass="mopen">(</span><spanclass="mord">3.3</span><spanclass="mclose">)</span></span></span></span></span></p><pclass=′katex−block′><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>17.64</mn><mo>+</mo><mn>27.96</mn><mo>+</mo><mn>6.93</mn></mrow><annotationencoding="application/x−tex">SA=17.64+27.96+6.93</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6833em;"></span><spanclass="mordmathnormal"style="margin−right:0.05764em;">S</span><spanclass="mordmathnormal">A</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">17.64</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">27.96</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">6.93</span></span></span></span></span></p><pclass=′katex−block′><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>52.53</mn><mtext> </mtext><mtext>sq. cm</mtext></mrow><annotationencoding="application/x−tex">SA=52.53 sq. cm</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.6833em;"></span><spanclass="mordmathnormal"style="margin−right:0.05764em;">S</span><spanclass="mordmathnormal">A</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.8389em;vertical−align:−0.1944em;"></span><spanclass="mord">52.53</span><spanclass="mspace"style="margin−right:0.1667em;"></span><spanclass="mordtext"><spanclass="mord">sq. cm</span></span></span></span></span></span></p>SA = 2lw + 2lh + 2wh </span></p> <p>where <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi>A</mi></mrow><annotation encoding="application/x-tex">SA</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">A</span></span></span></span> is the surface area, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi></mrow><annotation encoding="application/x-tex">l</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span></span></span></span> is the length, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi></mrow><annotation encoding="application/x-tex">w</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span></span></span></span> is the width, and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">h</span></span></span></span> is the height.</p> <h2><strong>Q: What are the dimensions of a rectangular prism?</strong></h2> <p>A: A rectangular prism has three dimensions: length, width, and height.</p> <h2><strong>Q: How do I calculate the area of each face of a rectangular prism?</strong></h2> <p>A: To calculate the area of each face of a rectangular prism, you can use the formula:</p> <ul> <li>Area of the front face: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>w</mi></mrow><annotation encoding="application/x-tex">lw</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">lw</span></span></span></span></li> <li>Area of the back face: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>w</mi></mrow><annotation encoding="application/x-tex">lw</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">lw</span></span></span></span></li> <li>Area of the top face: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mi>h</mi></mrow><annotation encoding="application/x-tex">wh</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mord mathnormal">h</span></span></span></span></li> <li>Area of the bottom face: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mi>h</mi></mrow><annotation encoding="application/x-tex">wh</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mord mathnormal">h</span></span></span></span></li> <li>Area of the left face: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>h</mi></mrow><annotation encoding="application/x-tex">lh</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">h</span></span></span></span></li> <li>Area of the right face: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>h</mi></mrow><annotation encoding="application/x-tex">lh</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">h</span></span></span></span></li> </ul> <h2><strong>Q: How do I add the areas of all the faces together to calculate the surface area of a rectangular prism?</strong></h2> <p>A: To add the areas of all the faces together, you can use the formula:</p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mi>l</mi><mi>w</mi><mo>+</mo><mi>l</mi><mi>w</mi><mo>+</mo><mi>w</mi><mi>h</mi><mo>+</mo><mi>w</mi><mi>h</mi><mo>+</mo><mi>l</mi><mi>h</mi><mo>+</mo><mi>l</mi><mi>h</mi></mrow><annotation encoding="application/x-tex">SA = lw + lw + wh + wh + lh + lh </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">lw</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">lw</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mord mathnormal">h</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mord mathnormal">h</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">h</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">h</span></span></span></span></span></p> <h2><strong>Q: Can I use a different method to calculate the surface area of a rectangular prism?</strong></h2> <p>A: Yes, you can use a different method to calculate the surface area of a rectangular prism. For example, you can calculate the area of each face and add them together.</p> <h2><strong>Q: What is the formula for the surface area of a rectangular prism in terms of the dimensions?</strong></h2> <p>A: The formula for the surface area of a rectangular prism in terms of the dimensions is:</p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>2</mn><mi>l</mi><mi>w</mi><mo>+</mo><mn>2</mn><mi>l</mi><mi>h</mi><mo>+</mo><mn>2</mn><mi>w</mi><mi>h</mi></mrow><annotation encoding="application/x-tex">SA = 2lw + 2lh + 2wh </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.0833em;"></span><span class="mord">2</span><span class="mord mathnormal" style="margin-right:0.02691em;">lw</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.0833em;"></span><span class="mord">2</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">h</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">2</span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mord mathnormal">h</span></span></span></span></span></p> <h2><strong>Q: Can I use the formula to calculate the surface area of a rectangular prism with different dimensions?</strong></h2> <p>A: Yes, you can use the formula to calculate the surface area of a rectangular prism with different dimensions.</p> <h2><strong>Q: What is the surface area of a rectangular prism with the following dimensions: Length = <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotation encoding="application/x-tex">4 \, \text{cm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">4</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">cm</span></span></span></span></span>, Width = <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotation encoding="application/x-tex">2 \, \text{cm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">cm</span></span></span></span></span>, and Height = <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotation encoding="application/x-tex">3 \, \text{cm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">cm</span></span></span></span></span>?</strong></h2> <p>A: To calculate the surface area of a rectangular prism with the given dimensions, you can use the formula:</p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>2</mn><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo><mo>+</mo><mn>2</mn><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo><mo>+</mo><mn>2</mn><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">SA = 2(4)(2) + 2(4)(3) + 2(2)(3) </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mopen">(</span><span class="mord">4</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mopen">(</span><span class="mord">4</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">3</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mopen">(</span><span class="mord">2</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">3</span><span class="mclose">)</span></span></span></span></span></p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>16</mn><mo>+</mo><mn>24</mn><mo>+</mo><mn>12</mn></mrow><annotation encoding="application/x-tex">SA = 16 + 24 + 12 </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">12</span></span></span></span></span></p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>52</mn><mtext> </mtext><mtext>sq. cm</mtext></mrow><annotation encoding="application/x-tex">SA = 52 \, \text{sq. cm} </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">52</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">sq. cm</span></span></span></span></span></span></p> <h2><strong>Q: Can I use the formula to calculate the surface area of a rectangular prism with different units of measurement?</strong></h2> <p>A: Yes, you can use the formula to calculate the surface area of a rectangular prism with different units of measurement.</p> <h2><strong>Q: What is the surface area of a rectangular prism with the following dimensions: Length = <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn><mtext> </mtext><mtext>in</mtext></mrow><annotation encoding="application/x-tex">5 \, \text{in}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6679em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">in</span></span></span></span></span>, Width = <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mtext> </mtext><mtext>in</mtext></mrow><annotation encoding="application/x-tex">3 \, \text{in}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6679em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">in</span></span></span></span></span>, and Height = <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mtext>in</mtext></mrow><annotation encoding="application/x-tex">2 \, \text{in}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6679em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">in</span></span></span></span></span>?</strong></h2> <p>A: To calculate the surface area of a rectangular prism with the given dimensions, you can use the formula:</p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>2</mn><mo stretchy="false">(</mo><mn>5</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo><mo>+</mo><mn>2</mn><mo stretchy="false">(</mo><mn>5</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo><mo>+</mo><mn>2</mn><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">SA = 2(5)(3) + 2(5)(2) + 2(3)(2) </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mopen">(</span><span class="mord">5</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">3</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mopen">(</span><span class="mord">5</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mopen">(</span><span class="mord">3</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">2</span><span class="mclose">)</span></span></span></span></span></p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>30</mn><mo>+</mo><mn>20</mn><mo>+</mo><mn>12</mn></mrow><annotation encoding="application/x-tex">SA = 30 + 20 + 12 </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">20</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">12</span></span></span></span></span></p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>62</mn><mtext> </mtext><mtext>sq. in</mtext></mrow><annotation encoding="application/x-tex">SA = 62 \, \text{sq. in} </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8623em;vertical-align:-0.1944em;"></span><span class="mord">62</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">sq. in</span></span></span></span></span></span></p> <h2><strong>Q: Can I use the formula to calculate the surface area of a rectangular prism with negative dimensions?</strong></h2> <p>A: No, you cannot use the formula to calculate the surface area of a rectangular prism with negative dimensions.</p> <h2><strong>Q: What is the surface area of a rectangular prism with the following dimensions: Length = <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>4</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotation encoding="application/x-tex">-4 \, \text{cm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">4</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">cm</span></span></span></span></span>, Width = <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>2</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotation encoding="application/x-tex">-2 \, \text{cm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">cm</span></span></span></span></span>, and Height = <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>3</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotation encoding="application/x-tex">-3 \, \text{cm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">cm</span></span></span></span></span>?</strong></h2> <p>A: Since the dimensions are negative, the surface area is not defined.</p> <h2><strong>Q: Can I use the formula to calculate the surface area of a rectangular prism with fractional dimensions?</strong></h2> <p>A: Yes, you can use the formula to calculate the surface area of a rectangular prism with fractional dimensions.</p> <h2><strong>Q: What is the surface area of a rectangular prism with the following dimensions: Length = <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4.5</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotation encoding="application/x-tex">4.5 \, \text{cm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">4.5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">cm</span></span></span></span></span>, Width = <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2.5</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotation encoding="application/x-tex">2.5 \, \text{cm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2.5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">cm</span></span></span></span></span>, and Height = <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3.5</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotation encoding="application/x-tex">3.5 \, \text{cm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">3.5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">cm</span></span></span></span></span>?</strong></h2> <p>A: To calculate the surface area of a rectangular prism with the given dimensions, you can use the formula:</p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>2</mn><mo stretchy="false">(</mo><mn>4.5</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>2.5</mn><mo stretchy="false">)</mo><mo>+</mo><mn>2</mn><mo stretchy="false">(</mo><mn>4.5</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>3.5</mn><mo stretchy="false">)</mo><mo>+</mo><mn>2</mn><mo stretchy="false">(</mo><mn>2.5</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>3.5</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">SA = 2(4.5)(2.5) + 2(4.5)(3.5) + 2(2.5)(3.5) </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mopen">(</span><span class="mord">4.5</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">2.5</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mopen">(</span><span class="mord">4.5</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">3.5</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mopen">(</span><span class="mord">2.5</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">3.5</span><span class="mclose">)</span></span></span></span></span></p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>22.5</mn><mo>+</mo><mn>31.5</mn><mo>+</mo><mn>17.5</mn></mrow><annotation encoding="application/x-tex">SA = 22.5 + 31.5 + 17.5 </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">22.5</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">31.5</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">17.5</span></span></span></span></span></p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>71.5</mn><mtext> </mtext><mtext>sq. cm</mtext></mrow><annotation encoding="application/x-tex">SA = 71.5 \, \text{sq. cm} </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">71.5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">sq. cm</span></span></span></span></span></span></p> <h2><strong>Q: Can I use the formula to calculate the surface area of a rectangular prism with decimal dimensions?</strong></h2> <p>A: Yes, you can use the formula to calculate the surface area of a rectangular prism with decimal dimensions.</p> <h2><strong>Q: What is the surface area of a rectangular prism with the following dimensions: Length = <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4.2</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotation encoding="application/x-tex">4.2 \, \text{cm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">4.2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">cm</span></span></span></span></span>, Width = <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2.1</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotation encoding="application/x-tex">2.1 \, \text{cm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2.1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">cm</span></span></span></span></span>, and Height = <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3.3</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotation encoding="application/x-tex">3.3 \, \text{cm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">3.3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">cm</span></span></span></span></span>?</strong></h2> <p>A: To calculate the surface area of a rectangular prism with the given dimensions, you can use the formula:</p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>2</mn><mo stretchy="false">(</mo><mn>4.2</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>2.1</mn><mo stretchy="false">)</mo><mo>+</mo><mn>2</mn><mo stretchy="false">(</mo><mn>4.2</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>3.3</mn><mo stretchy="false">)</mo><mo>+</mo><mn>2</mn><mo stretchy="false">(</mo><mn>2.1</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>3.3</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">SA = 2(4.2)(2.1) + 2(4.2)(3.3) + 2(2.1)(3.3) </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mopen">(</span><span class="mord">4.2</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">2.1</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mopen">(</span><span class="mord">4.2</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">3.3</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mopen">(</span><span class="mord">2.1</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord">3.3</span><span class="mclose">)</span></span></span></span></span></p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>17.64</mn><mo>+</mo><mn>27.96</mn><mo>+</mo><mn>6.93</mn></mrow><annotation encoding="application/x-tex">SA = 17.64 + 27.96 + 6.93 </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">17.64</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">27.96</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">6.93</span></span></span></span></span></p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>S</mi><mi>A</mi><mo>=</mo><mn>52.53</mn><mtext> </mtext><mtext>sq. cm</mtext></mrow><annotation encoding="application/x-tex">SA = 52.53 \, \text{sq. cm} </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">52.53</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">sq. cm</span></span></span></span></span></span></p>