Given that AB=2, CD=4, and that line AB and line CD are diameters of the respective semicircles below, find the area of the shaded region.

Guest Feb 4, 2022

#1**0 **

Let the center of CD be O. From O to A and O to B, OA = OB = 2. Thus OAB is an equilateral triangle: Area = 1.732

Area of sector OAB = (1/6)(pi)(4) = 2.094. Area of segment AB = 2.094 - 1.732 = 0.362.

Area of semicircle with diameter AB = 1.571

Area of reqd shaded region = 1.571 - 0.362 = 1.209.

Guest Feb 4, 2022