The Area Of A Trapezoid Is 70.55 Square Feet. The Lengths Of The Bases Are 11.4 Feet And 5.6 Feet. What Is The Height Of The Trapezoid?A. 4.15 FtB. $4.15 \, \text{ft}^2$C. 8.3 FtD. $8.3 \, \text{ft}^2$

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Understanding the Problem

The area of a trapezoid is given as 70.55 square feet, and the lengths of its bases are 11.4 feet and 5.6 feet. We are asked to find the height of the trapezoid. To solve this problem, we need to use the formula for the area of a trapezoid, which is:

A = (1/2) × (a + b) × h

where A is the area, a and b are the lengths of the bases, and h is the height.

Applying the Formula

We are given the area (A = 70.55 square feet) and the lengths of the bases (a = 11.4 feet and b = 5.6 feet). We need to substitute these values into the formula and solve for the height (h).

70.55 = (1/2) × (11.4 + 5.6) × h

Simplifying the Equation

First, let's simplify the equation by calculating the sum of the bases:

11.4 + 5.6 = 17

Now, substitute this value back into the equation:

70.55 = (1/2) × 17 × h

Solving for the Height

To solve for the height (h), we need to isolate h on one side of the equation. Multiply both sides of the equation by 2 to eliminate the fraction:

141.1 = 17 × h

Next, divide both sides of the equation by 17 to solve for h:

h = 141.1 ÷ 17

Calculating the Height

Now, let's calculate the height:

h = 8.3

The height of the trapezoid is 8.3 feet.

Conclusion

In this problem, we used the formula for the area of a trapezoid to find the height. We were given the area and the lengths of the bases, and we were able to solve for the height by substituting the values into the formula and simplifying the equation. The height of the trapezoid is 8.3 feet.

Answer

The correct answer is:

  • C. 8.3 ft

This answer is based on the calculation of the height using the formula for the area of a trapezoid.

Understanding the Basics

In our previous article, we discussed how to find the height of a trapezoid using the formula for the area of a trapezoid. In this article, we will answer some frequently asked questions about the area of a trapezoid.

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

A: The formula for the area of a trapezoid is:

A = (1/2) × (a + b) × h

where A is the area, a and b are the lengths of the bases, and h is the height.

Q: What are the lengths of the bases?

A: The lengths of the bases are the two parallel sides of the trapezoid. In our previous example, the lengths of the bases were 11.4 feet and 5.6 feet.

Q: How do I find the height of a trapezoid?

A: To find the height of a trapezoid, you need to use the formula for the area of a trapezoid. Substitute the values of the area, the lengths of the bases, and solve for the height.

Q: What if I don't know the lengths of the bases?

A: If you don't know the lengths of the bases, you can't find the height of the trapezoid using the formula. You need to know the lengths of the bases to use the formula.

Q: Can I use the formula for the area of a trapezoid to find the lengths of the bases?

A: No, you can't use the formula for the area of a trapezoid to find the lengths of the bases. The formula is used to find the height of the trapezoid, not the lengths of the bases.

Q: What if the trapezoid is not a right trapezoid?

A: The formula for the area of a trapezoid only works for right trapezoids. If the trapezoid is not a right trapezoid, you need to use a different formula to find the area.

Q: Can I use the formula for the area of a trapezoid to find the area of a triangle?

A: No, you can't use the formula for the area of a trapezoid to find the area of a triangle. The formula is specific to trapezoids and doesn't work for triangles.

Q: What if I have a trapezoid with a non-parallel side?

A: If you have a trapezoid with a non-parallel side, it's not a trapezoid. A trapezoid by definition has two parallel sides.

Conclusion

In this article, we answered some frequently asked questions about the area of a trapezoid. We discussed the formula for the area of a trapezoid, how to find the height of a trapezoid, and some common misconceptions about trapezoids.

Common Misconceptions

  • The formula for the area of a trapezoid only works for right trapezoids.
  • You can use the formula for the area of a trapezoid to find the lengths of the bases.
  • The formula for the area of a trapezoid can be used to find the area of a triangle.

Answer

The correct answers to the questions are:

  • Q: What is the formula for the area of a trapezoid? A: A = (1/2) × (a + b) × h
  • Q: What are the lengths of the bases? A: 11.4 feet and 5.6 feet
  • Q: How do I find the height of a trapezoid? A: Use the formula for the area of a trapezoid
  • Q: What if I don't know the lengths of the bases? A: You can't find the height of the trapezoid
  • Q: Can I use the formula for the area of a trapezoid to find the lengths of the bases? A: No
  • Q: What if the trapezoid is not a right trapezoid? A: You need to use a different formula
  • Q: Can I use the formula for the area of a trapezoid to find the area of a triangle? A: No
  • Q: What if I have a trapezoid with a non-parallel side? A: It's not a trapezoid