Find the area of the shaded regions:

Question

Answer 1

the shaded area is the area of the semicircle minus the area of the triangle. The area of of the semicircle is

pi(4Sq)/2=8pi

To calculate the area of the triangle we need to drop an altitude from C to the diameter and label that point d. we then have 2 congruent triangles CDB and COD

So OD=DB=2

Now we can solve for the altitude 4sq=2sq + xs

Xsq= 12 x = sq rt12 Area if triangle = (1/2)base x altitude = (1/2) (8)(sq rt 12)= 4sqrt 12

shaded area is 8pi - 4sqrt 12