Answer
The area of the shaded region is $\approx 232.8$ in$^{2}$.
Work Step by Step
1. Find area of the semicircle
Let $S =$ area of the semicircle
(Note: Radius $= diameter \div 2 = 18 \div 2= 9$ in.)
$S = \frac{1}{2}\pi r^{2}$
$S = \frac{1}{2}(3.14)(9^{2})$
$S = 254.34 \times 0.5$
$S = 127.17$ in$^{2}$
2. Find the rectangle
Let $R =$ area of the rectangle
$R = length \times width$
$R = 20 \times 18$
$R = 360$ in$^{2}$
3. Find the area of the shaded region by subtracting the area of the rectangle from the area of the semicircle
Let $A =$ area of the shaded region
$A = R - S$
$A = 360 - 127.17$
$A = 232.83$ in$^{2}$
$A \approx 232.8$ in$^{2}$
