Question

What is the area of this trapezoid?

Responses

96 in²
96 in²

132 in²
132 in²

168 in²
168 in²

1344 in²
1344 in²
Trapezoid A B C D with parallel sides D C and A B. Points F and E are between D and C. F E B A form a rectangle with 4 right angles. D F is 3 inches, F E is 8 inches., E C is 3 inches., E B is 12 inches., and A B is 8 inches.

Answer 1

To find the area of trapezoid ABCD, we can use the formula for the area of a trapezoid, which is:

\[
\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h
\]

Where:
- \(b_1\) and \(b_2\) are the lengths of the two parallel sides,
- \(h\) is the height of the trapezoid.

In this case, sides \(DC\) and \(AB\) are the parallel sides.

From the information given:
- Length of \(AB = 8\) inches.
- Length of \(DC = DF + FE + EC = 3 + 8 + 3 = 14\) inches.
- The height \(h\) is the vertical distance between the parallel sides, which is the same as the length of \(EB = 12\) inches.

Now, we can substitute these values into the area formula:

\[
\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h
\]
\[
\text{Area} = \frac{1}{2} \times (8 + 14) \times 12
\]
\[
\text{Area} = \frac{1}{2} \times 22 \times 12
\]
\[
\text{Area} = 11 \times 12 = 132 \text{ in}^2
\]

Therefore, the area of the trapezoid is **132 in²**.