Part A:
Recall that the area of a trapezoid is given by
[tex]A=\frac{(a+b)_{}}{2}\times h[/tex]
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.
[tex]\begin{gathered} A=\frac{(50+100)_{}}{2}\times25 \\ A=\frac{150_{}}{2}\times25 \\ A=75\times25 \\ A=1875\: in^2 \end{gathered}[/tex]
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.
[tex]\begin{gathered} A=4\times1875 \\ A=7500\: in^2 \end{gathered}[/tex]
Therefore, the area of the entire trapezoid is 7500 inches squared.
