Expression For Surface Area Of Attic:$\[ 45(40+25+25) + \frac{1}{2}(40 \times 15) \\]Click The Arrows To Choose An Answer From Each Menu To Explain Your Reasoning.1. The Net Linda Drew Is: [Choose]2. The First Term Of Linda's Expression,...
Introduction
In mathematics, the surface area of a three-dimensional object is a crucial concept that helps us calculate the total area of its surface. When it comes to an attic, the surface area is essential for determining the amount of material needed for roofing, insulation, or any other purpose. In this article, we will delve into the expression for the surface area of an attic and break it down step by step.
The Net Linda Drew
To start with, let's consider the net Linda drew, which is a representation of the attic's surface area. The net is a two-dimensional representation of the three-dimensional object, showing the various faces and their dimensions.
Choosing the Correct Net
When choosing the correct net, we need to consider the shape and dimensions of the attic. The net should accurately represent the attic's surface area, taking into account the various faces, edges, and vertices.
- Option 1: A rectangular net with dimensions 40 x 25 x 15
- Option 2: A triangular net with dimensions 40 x 25 x 15
- Option 3: A trapezoidal net with dimensions 40 x 25 x 15
Based on the given dimensions, the correct net is the rectangular net with dimensions 40 x 25 x 15.
The First Term of Linda's Expression
Now that we have chosen the correct net, let's move on to the first term of Linda's expression. The first term represents the area of the rectangular faces of the attic.
Calculating the Area of Rectangular Faces
To calculate the area of the rectangular faces, we need to multiply the length and width of each face.
- Area of the first rectangular face: 40 x 25 = 1000
- Area of the second rectangular face: 40 x 25 = 1000
- Area of the third rectangular face: 25 x 15 = 375
The total area of the rectangular faces is the sum of the areas of the individual faces.
Calculating the Total Area of Rectangular Faces
To calculate the total area of the rectangular faces, we need to add the areas of the individual faces.
- Total area of rectangular faces: 1000 + 1000 + 375 = 2375
The first term of Linda's expression is 45 times the total area of the rectangular faces.
Calculating the First Term of Linda's Expression
To calculate the first term of Linda's expression, we need to multiply 45 by the total area of the rectangular faces.
- First term of Linda's expression: 45 x 2375 = 106625
The Second Term of Linda's Expression
Now that we have calculated the first term of Linda's expression, let's move on to the second term. The second term represents the area of the triangular faces of the attic.
Calculating the Area of Triangular Faces
To calculate the area of the triangular faces, we need to multiply the base and height of each face.
- Area of the first triangular face: 40 x 15/2 = 300
- Area of the second triangular face: 25 x 15/2 = 187.5
The total area of the triangular faces is the sum of the areas of the individual faces.
Calculating the Total Area of Triangular Faces
To calculate the total area of the triangular faces, we need to add the areas of the individual faces.
- Total area of triangular faces: 300 + 187.5 = 487.5
The second term of Linda's expression is 1/2 times the total area of the triangular faces.
Calculating the Second Term of Linda's Expression
To calculate the second term of Linda's expression, we need to multiply 1/2 by the total area of the triangular faces.
- Second term of Linda's expression: 1/2 x 487.5 = 243.75
The Final Expression for Surface Area
Now that we have calculated the first and second terms of Linda's expression, let's combine them to get the final expression for the surface area of the attic.
Combining the First and Second Terms
To combine the first and second terms, we need to add them together.
- Final expression for surface area: 106625 + 243.75 = 106868.75
The final expression for the surface area of the attic is 106868.75.
Conclusion
Q: What is the surface area of an attic?
A: The surface area of an attic is the total area of its surface, including the roof, walls, and floor.
Q: Why is the surface area of an attic important?
A: The surface area of an attic is important because it helps determine the amount of material needed for roofing, insulation, or any other purpose.
Q: What is the expression for the surface area of an attic?
A: The expression for the surface area of an attic is 45(40+25+25) + 1/2(40 x 15).
Q: How do I calculate the first term of Linda's expression?
A: To calculate the first term of Linda's expression, you need to multiply 45 by the total area of the rectangular faces. The total area of the rectangular faces is 2375, so the first term is 45 x 2375 = 106625.
Q: How do I calculate the second term of Linda's expression?
A: To calculate the second term of Linda's expression, you need to multiply 1/2 by the total area of the triangular faces. The total area of the triangular faces is 487.5, so the second term is 1/2 x 487.5 = 243.75.
Q: What is the final expression for the surface area of the attic?
A: The final expression for the surface area of the attic is 106868.75.
Q: How do I choose the correct net for the attic?
A: To choose the correct net for the attic, you need to consider the shape and dimensions of the attic. The net should accurately represent the attic's surface area, taking into account the various faces, edges, and vertices.
Q: What are the dimensions of the rectangular net?
A: The dimensions of the rectangular net are 40 x 25 x 15.
Q: What are the dimensions of the triangular net?
A: The dimensions of the triangular net are 40 x 25 x 15.
Q: What are the dimensions of the trapezoidal net?
A: The dimensions of the trapezoidal net are 40 x 25 x 15.
Q: Which net is the correct choice for the attic?
A: The correct net for the attic is the rectangular net with dimensions 40 x 25 x 15.
Q: How do I calculate the area of the rectangular faces?
A: To calculate the area of the rectangular faces, you need to multiply the length and width of each face.
Q: How do I calculate the area of the triangular faces?
A: To calculate the area of the triangular faces, you need to multiply the base and height of each face.
Q: What is the total area of the rectangular faces?
A: The total area of the rectangular faces is 2375.
Q: What is the total area of the triangular faces?
A: The total area of the triangular faces is 487.5.
Q: What is the final answer for the surface area of the attic?
A: The final answer for the surface area of the attic is 106868.75.