Question

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

Explanation:

Step1: Recall the formula for the area of a trapezoid

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

Step2: Identify the values of \(a\), \(b\), and \(h\)

From the diagram, the two parallel sides (bases) are \(a = 4\) ft and \(b = 13\) ft, and the height \(h = 4\) ft.

Step3: Substitute the values into the formula

Substitute \(a = 4\), \(b = 13\), and \(h = 4\) into the formula:
\[

$$\begin{align*} A&=\frac{(4 + 13)}{2} \times 4\\ &=\frac{17}{2} \times 4\\ &= 17\times2\\ &= 34 \end{align*}$$

\]

Answer:

The area of the trapezoid is \(34\) square feet (or \(34\) ft\(^2\)).