Carcass wrote:

In the figure above, AC = BC = 8, angle C = 90°, and the circular arc has its center at point C. Find the area of the shaded region.
A. \(8\pi-32\)
B. \(16\pi-32\)
C. \(16\pi-64\)
D. \(32\pi-32\)
E. \(32\pi-64\)
Area of shaded region = (
area of sector) - (
area of triangle)
Area of circle = π(radius)²
Area of triangle = (base)(height)/2The sector ABC is 1/4 of a circle of radius 8
So,
area of sector = (1/4)(π)(8²)
= 16π area of triangle = (8)(8)/2
= 32So, area of shaded region = (
16π) - (
32)
Answer: B
Cheers,
Brent