Question

find the area of this trapezoid. be sure to include the correct unit in your answer.

Explanation:

Step1: Recall trapezoid area formula

The formula for the area of a trapezoid is $A = \frac{1}{2}(b_1 + b_2)h$, where $b_1$ and $b_2$ are the lengths of the two parallel sides (bases), and $h$ is the height (the perpendicular distance between the bases).

Step2: Identify $b_1$, $b_2$, and $h$

From the diagram, the two parallel sides (bases) have lengths $b_1 = 5$ yd and $b_2 = 19$ yd, and the height $h = 4$ yd.

Step3: Substitute values into the formula

Substitute $b_1 = 5$, $b_2 = 19$, and $h = 4$ into the formula:
\[

$$\begin{align*} A&=\frac{1}{2}(5 + 19)\times4\\ &=\frac{1}{2}(24)\times4\\ &= 12\times4\\ &= 48 \end{align*}$$

\]

Answer:

The area of the trapezoid is $\boldsymbol{48}$ square yards.