Question

AREA ADDITION AND SUBTRACTION URGENT?

Answer 1

The area of shaded region is

$A_{shaded}=A_{circle}-A_{segment}$.

Find the area of circle and segment:

$A_{circle}=\pi r^2=\pi (8.35)^2=69.7225\pi=219.0397,\\ A_{segment}=A_{sector}-A_{triangle},\\ \\A_{sector}=\dfrac{r^2 \alpha}{2} =\dfrac{(8.35)^2\cdot \frac{5}{9}\pi}{2}=19.3674\pi=60.8445,\\ \\A_{triangle}=\dfrac{1}{2}r^2\sin \alpha=\dfrac{1}{2}(8.35)^2\sin 100^{\circ}=34.3316,\\ \\A_{segment}=60.8445-34.3316=26.5129$.

Then $A_{shaded}=A_{circle}-A_{segment} =219.0397-26.5129=192.5268$.

The area of shaded region rounded to the nearest tenth is 192.5 sq. ft.

Answer: 192.5 sq. ft.