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.
$$A.\ 8\pi-32$$
$$B.\ 16\pi-32$$
$$C.\ 16\pi-64$$
$$D.\ 32\pi-32$$
$$E.\ 32\pi-64$$
The OA is B.
In this PS question, I just need to find the area of the circular arc and then subtract the area of the triangle, right?
It will be,
$$A_{ARC}-A_{\triangle}=\frac{1}{2}r^2\theta-\frac{1}{2}b\cdot h=\frac{1}{2}8^2\frac{\pi}{2}-\frac{1}{2}8\cdot8=16\pi-32$$
Is there a strategic approach to this question? Can any experts help me, please?
