The figure shows circle O with diameter AB and inscribed angle ABC with AB = 8 and BC = 4. When the area of the shaded region, in square units, is expressed in the form a + bπ, what is the value of ab?
+128460 In triangle ABC, angle BCA = 90°
And the shaded area is composed of equilateral triangle BOC (BO = BC = CO = 4) plus sector COA
Area of triangle BOC = (1/2) 4^2 sin 60° = 8sqrt (3) / 2 = 4sqrt (3)
Area of sector COA = (1/3)area of circle = (1/3) pi (4^2) = (16/3) pi
Total area = 4sqrt (3) + (16/3) pi
ab = (4sqrt 3) ( 16/3) = 64 / sqrt 3
