Question

Find the area of a trapezoid that has a perimeter of 46, a base length of 13, another base length of 5, and a non-base length of 10. The height of the trapezoid is 9. What is the trapezoid’s area?(1 point)
Responses

162 units2
162 units squared

81 units2
81 units squared

117 units2
117 units squared

18 units2

Answer 1

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

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

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

From the information given:

- Base length \(b_1 = 13\)
- Base length \(b_2 = 5\)
- Height \(h = 9\)

Now, plug in the values to calculate the area:

\[
\text{Area} = \frac{1}{2} \times (13 + 5) \times 9
\]

Calculating the sum of the bases:

\[
13 + 5 = 18
\]

Now substitute that back into the area formula:

\[
\text{Area} = \frac{1}{2} \times 18 \times 9
\]

Calculate \( \frac{1}{2} \times 18 \):

\[
\frac{1}{2} \times 18 = 9
\]

Now multiply by the height:

\[
\text{Area} = 9 \times 9 = 81
\]

Thus, the area of the trapezoid is:

\[
\boxed{81 \text{ units}^2}
\]