In the figure below, O is the center of the circle, and the radius of the circle is 8. Angle BOA is right. What is the area of the filled-in (purple) region?
Explain the steps of your solution. Give your answer in exact form (which may involve pi). In other words, don't round off (but do simplify if you can).
The area if the whole sector is just (1/4) that of the circle (since BOA is a right angle )
So...area of the sector = (1/4) pi * radius^2 = (1/4) pi * 8^2 = (1/4) pi * 64 = (1/4) * 64 * pi = 16 pi units'^2
The area of the triangle AOB is just (1/2) radius^2 = (1/2) (8)^2 = (1/2) 64 = 32 units^2
So....the purple area is just the area of the sector - area of the triangle AOB =
[ 16 pi - 32] units^2 ≈ 18.26 units^2