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)=(r^2 \alpha)/(2) =((8.35)^2\cdot (5)/(9)\pi)/(2)=19.3674\pi=60.8445,\\ \\A_(triangle)=(1)/(2)r^2\sin \alpha=(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.