Question

What is the area of the trapezoid? If necessary, round your answer to the nearest tenth.

A trapezoid with bottom side length of 8.5 feet, top side length of 5.5 feet, and height of 6.5 feet.
35.8 feet squared
45.5 feet squared
46.8 feet squared
55.3 feet squared

Answer 1

To find the area of a trapezoid, you can use the formula:

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

where \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides (bases) and \( h \) is the height.

In this problem:
- \( b_1 = 8.5 \) feet (bottom side)
- \( b_2 = 5.5 \) feet (top side)
- \( h = 6.5 \) feet (height)

Now plug in the values:

\[
\text{Area} = \frac{1}{2} \times (8.5 + 5.5) \times 6.5
\]

Calculate \( 8.5 + 5.5 \):

\[
8.5 + 5.5 = 14
\]

Now substitute this back into the area formula:

\[
\text{Area} = \frac{1}{2} \times 14 \times 6.5
\]

Now calculate \( \frac{1}{2} \times 14 \):

\[
\frac{1}{2} \times 14 = 7
\]

Now multiply by the height:

\[
\text{Area} = 7 \times 6.5 = 45.5
\]

Therefore, the area of the trapezoid is:

\[
\text{Area} = 45.5 \text{ feet squared}
\]

The correct answer is **45.5 feet squared**.