Find the area of the shaded regions below. give your answer as a completely simplified exact value in terms of π (no approximations).

Find the area of the circle.

If the radius is 4cm, then we can use the equation π r^2

π (4)^2

4^2 = 16

16π

Find the area of half the circle.

Cut that in half

8π

Find the area of the two triangles.

Then subtract those, and you're done!

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2