+1348 Plz help with semicircles
Semicircles are drawn on diameters $\overline{AB}$ and $\overline{CD},$ as shown below. Find the area of the shaded region.
+129895 
EF = sqrt (2^2 - (sqrt 3)^2) = sqrt ( 4 -3) = sqrt (1) = 1
Area of triangle FBE = (1/2) (AB) (EF) = (1/2)(2sqrt 3) ( 1) = sqrt (3)
tan (angle BFE) = sqrt (3) / 1 = sqrt (3)
arctan (sqrt (3)) = 60° = measure of angle BFE
So angle AEB = 120°
Area of sector AEB = pi * 2^2 / 3 = (4/3)pi
Area between sector AEB and triangle FBE = (4/3)pi - sqrt (3) (1)
Area of small semi-circle = pi (sqrt 3)^2 / 2 = (3/2) pi (2)
Shaded area = (2) - (1) = (3/2) pi - [ (4/3) pi - sqrt (3) ] = pi/6 + sqrt (3)
