Question

A trapezoid has one pair of opposite parallel sides and one pair of opposite non-parallel sides. The pair of parallel sides has lengths 15 yd. and 19 yd. The non-parallel sides have lengths of 11 yd. and 8 yd. The distance between the parallel sides is 12 yd. What is the are of the trapezoid?
___yd.^2

Answer 1

To find the area of a trapezoid, we 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, and \( h \) is the height (the distance between the parallel sides).

In this case, we have:
- \( b_1 = 15 \, \text{yd} \)
- \( b_2 = 19 \, \text{yd} \)
- \( h = 12 \, \text{yd} \)

Now, we can substitute these values into the formula:

\[
\text{Area} = \frac{1}{2} \times (15 + 19) \times 12
\]

First, we calculate the sum of the lengths of the parallel sides:

\[
15 + 19 = 34
\]

Next, we substitute this sum into the area formula:

\[
\text{Area} = \frac{1}{2} \times 34 \times 12
\]

Calculating \( \frac{1}{2} \times 34 \):

\[
\frac{1}{2} \times 34 = 17
\]

Now, we multiply by the height:

\[
\text{Area} = 17 \times 12
\]

Calculating this gives:

\[
17 \times 12 = 204
\]

Thus, the area of the trapezoid is:

\[
\boxed{204} \text{ yd}^2
\]