To Find The Area Of A Trapezoid, Dylan Uses The Formula $A = \frac{1}{2}(b_1 + B_2)h$. The Bases Have Lengths Of $3.6 \, \text{cm}$ And $12 \frac{1}{3} \, \text{cm}$. The Height Of The Trapezoid Is $\sqrt{5} \,

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Introduction

In mathematics, a trapezoid is a quadrilateral with at least one pair of parallel sides. The formula for finding the area of a trapezoid is given by A=12(b1+b2)hA = \frac{1}{2}(b_1 + b_2)h, where b1b_1 and b2b_2 are the lengths of the two parallel sides, and hh is the height of the trapezoid. In this article, we will explore how to use this formula to find the area of a trapezoid.

The Formula for the Area of a Trapezoid

The formula for the area of a trapezoid is given by A=12(b1+b2)hA = \frac{1}{2}(b_1 + b_2)h. This formula is derived from the fact that the area of a trapezoid can be divided into two triangles and a rectangle. The two triangles have bases b1b_1 and b2b_2 and height hh, while the rectangle has base b1+b2b_1 + b_2 and height hh. By adding the areas of the two triangles and the rectangle, we get the formula for the area of a trapezoid.

Converting Mixed Numbers to Decimal Form

In the problem, the length of one of the bases is given as 1213 cm12 \frac{1}{3} \, \text{cm}. To use this value in the formula, we need to convert it to decimal form. To do this, we can divide the numerator by the denominator: 13=0.33…\frac{1}{3} = 0.33\ldots. Therefore, the length of the base is 12+0.33…=12.33… cm12 + 0.33\ldots = 12.33\ldots \, \text{cm}.

Finding the Area of the Trapezoid

Now that we have the lengths of the two bases and the height of the trapezoid, we can use the formula to find the area. Plugging in the values, we get:

A=12(3.6+12.33…)5A = \frac{1}{2}(3.6 + 12.33\ldots)\sqrt{5}

To evaluate this expression, we need to add the lengths of the two bases: 3.6+12.33…=15.93…3.6 + 12.33\ldots = 15.93\ldots. Then, we can multiply this value by the height: 15.93…×5=15.93…×2.236…=35.59…15.93\ldots \times \sqrt{5} = 15.93\ldots \times 2.236\ldots = 35.59\ldots. Finally, we can multiply this value by 12\frac{1}{2} to get the area:

A=12×35.59…=17.795…A = \frac{1}{2} \times 35.59\ldots = 17.795\ldots

Conclusion

In this article, we have explored how to use the formula for the area of a trapezoid to find the area of a trapezoid with given lengths of the two parallel sides and the height. We have also seen how to convert mixed numbers to decimal form and how to evaluate expressions involving square roots.

Real-World Applications

The formula for the area of a trapezoid has many real-world applications. For example, it can be used to find the area of a trapezoidal-shaped roof or a trapezoidal-shaped garden bed. It can also be used to find the area of a trapezoidal-shaped piece of land or a trapezoidal-shaped building.

Tips and Tricks

Here are some tips and tricks for using the formula for the area of a trapezoid:

  • Make sure to convert mixed numbers to decimal form before using them in the formula.
  • Use a calculator to evaluate expressions involving square roots.
  • Check your work by plugging in the values and evaluating the expression.
  • Use the formula to find the area of a trapezoid with given lengths of the two parallel sides and the height.

Common Mistakes

Here are some common mistakes to avoid when using the formula for the area of a trapezoid:

  • Failing to convert mixed numbers to decimal form.
  • Failing to use a calculator to evaluate expressions involving square roots.
  • Failing to check your work by plugging in the values and evaluating the expression.
  • Failing to use the formula to find the area of a trapezoid with given lengths of the two parallel sides and the height.

Conclusion

Q: What is the formula for the area of a trapezoid?

A: The formula for the area of a trapezoid is given by A=12(b1+b2)hA = \frac{1}{2}(b_1 + b_2)h, where b1b_1 and b2b_2 are the lengths of the two parallel sides, and hh is the height of the trapezoid.

Q: How do I convert mixed numbers to decimal form?

A: To convert a mixed number to decimal form, you can divide the numerator by the denominator. For example, to convert 121312 \frac{1}{3} to decimal form, you can divide 1 by 3: 13=0.33…\frac{1}{3} = 0.33\ldots. Therefore, the decimal form of 121312 \frac{1}{3} is 12+0.33…=12.33…12 + 0.33\ldots = 12.33\ldots.

Q: How do I evaluate expressions involving square roots?

A: To evaluate an expression involving a square root, you can use a calculator or simplify the expression by multiplying the numerator and denominator by the square root of the number. For example, to evaluate 5\sqrt{5}, you can multiply the numerator and denominator by 5\sqrt{5}: 51×55=55\frac{\sqrt{5}}{1} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{5}{\sqrt{5}}.

Q: What are some common mistakes to avoid when using the formula for the area of a trapezoid?

A: Some common mistakes to avoid when using the formula for the area of a trapezoid include:

  • Failing to convert mixed numbers to decimal form.
  • Failing to use a calculator to evaluate expressions involving square roots.
  • Failing to check your work by plugging in the values and evaluating the expression.
  • Failing to use the formula to find the area of a trapezoid with given lengths of the two parallel sides and the height.

Q: How do I check my work when using the formula for the area of a trapezoid?

A: To check your work when using the formula for the area of a trapezoid, you can plug in the values and evaluate the expression. For example, if you are given the lengths of the two parallel sides and the height, you can plug these values into the formula and evaluate the expression to get the area.

Q: What are some real-world applications of the formula for the area of a trapezoid?

A: Some real-world applications of the formula for the area of a trapezoid include:

  • Finding the area of a trapezoidal-shaped roof or a trapezoidal-shaped garden bed.
  • Finding the area of a trapezoidal-shaped piece of land or a trapezoidal-shaped building.
  • Finding the area of a trapezoidal-shaped object or a trapezoidal-shaped surface.

Q: How do I use the formula for the area of a trapezoid to find the area of a trapezoid with given lengths of the two parallel sides and the height?

A: To use the formula for the area of a trapezoid to find the area of a trapezoid with given lengths of the two parallel sides and the height, you can follow these steps:

  1. Plug in the values of the lengths of the two parallel sides and the height into the formula.
  2. Evaluate the expression to get the area.
  3. Check your work by plugging in the values and evaluating the expression.

Q: What are some tips and tricks for using the formula for the area of a trapezoid?

A: Some tips and tricks for using the formula for the area of a trapezoid include:

  • Make sure to convert mixed numbers to decimal form before using them in the formula.
  • Use a calculator to evaluate expressions involving square roots.
  • Check your work by plugging in the values and evaluating the expression.
  • Use the formula to find the area of a trapezoid with given lengths of the two parallel sides and the height.

Conclusion

In conclusion, the formula for the area of a trapezoid is a useful tool for finding the area of a trapezoid with given lengths of the two parallel sides and the height. By following the tips and tricks outlined in this article, you can avoid common mistakes and find the area of a trapezoid with ease.