The triangle is a 3-4-5 right triangle (times 8), so the diameter is 40 in.
The area of the semicircle is
.. (1/2)π(20 in)^2 = 200π in^2
The area of the triangle is
.. (1/2)*(24 in)*(32 in) = 384 in^2
The shaded area is the difference
.. (200π -384) in^2
