What is the area of a semicircle with a diameter of $16$ inches?

Area of semicircle = $\frac{1}{2} \times $ area of circle $= \frac{\pi r^2}{2} $

Diameter $=16$ inches $\implies $ radius $=8$ inches

Required Area $=\frac{\pi r^2}{2} = \frac{\pi \times 8^2}{2} = 32\pi $ square inches.

Option (A) is correct.