The area of shaded region is
[tex] A_{shaded}=A_{circle}-A_{segment} [/tex].
Find the area of circle and segment:
[tex] 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 [/tex].
Then [tex] A_{shaded}=A_{circle}-A_{segment} =219.0397-26.5129=192.5268[/tex].
The area of shaded region rounded to the nearest tenth is 192.5 sq. ft.
Answer: 192.5 sq. ft.
