Question

find the perimeter and area of the trapezoid shown below. round your answer to the nearest hundredth as needed.
the perimeter is
feet.
the area is
square feet.
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Explanation:

Step1: Calculate the perimeter

The perimeter of a trapezoid is the sum of all its side lengths. The sides are \(7.8\) ft, \(16.1\) ft, \(19.5\) ft, and \(17.4\) ft.
\[

$$\begin{align*} \text{Perimeter} &= 7.8 + 16.1 + 19.5 + 17.4\\ &= 23.9 + 19.5 + 17.4\\ &= 43.4 + 17.4\\ &= 60.8 \end{align*}$$

\]

Step2: Calculate the area

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a\) and \(b\) are the lengths of the two parallel sides (bases), and \(h\) is the height. Here, \(a = 7.8\) ft, \(b = 19.5\) ft, and \(h = 15.6\) ft.
\[

$$\begin{align*} A&=\frac{(7.8 + 19.5)\times15.6}{2}\\ &=\frac{27.3\times15.6}{2}\\ &=\frac{425.88}{2}\\ & = 212.94 \end{align*}$$

\]

Answer:

The perimeter is \(60.8\) feet.
The area is \(212.94\) square feet.