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).
+128474
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
