Area of semicircle adjacent to a square

Question

Find the area of the given figure. The figure is a semicircle adjacent to a square. The square has sides of length 32 cm.

Answer 1

If the semicircle is adjacent to the square, that means that the semicircle has a diameter equal to the length of the square, which is 32 cm.

The formula for the area of a circle is pi times the radius squared. Because the diameter of the semicircle is 32, the radius is half of that, or 16. So the area of the semicircle is 16^2, or 256, times pi. Lastly, because a semicircle is half of a circle, we must divide this area by 2. So our area is 128 times pi centimeters squared.