Question

Part A. what is the area of one trapezoid? Part B. What is the area of the entire bench?

Answer 1

Part A:

Recall that the area of a trapezoid is given by

`A=\frac{(a+b)_{}}{2}* h`

Where a and b are the lengths of the parallel sides, and h is the height between them.

From the figure, we see that,

a = 50 in

b = 100 in

h = 25 in

Let us substitute these values into the above formula.

`\begin{gathered} A=\frac{(50+100)_{}}{2}*25 \\ A=\frac{150_{}}{2}*25 \\ A=75*25 \\ A=1875\: in^2 \end{gathered}`

Therefore, the area of one trapezoid is 1875 inches squared.

Part B:

The bench is made up of four trapezoids

Since we know the area of one trapezoid so we multiply it by 4 to get the area of the entire bench.

`\begin{gathered} A=4*1875 \\ A=7500\: in^2 \end{gathered}`

Therefore, the area of the entire trapezoid is 7500 inches squared.