Question

In the square below, the two semi-circles are congruent. Find the area of the shaded region. If necessary, round your answer to two decimal places.
the square side measures at 8in

Answer 1

Let's start with the area of the square
$area \: square = s \times s = 8 \times 8 = 64$
now let's subtract the are of the two half circles.
two half circles are the same as one circle, and we know that the diameter of the circle is 8 (same as the side of a square) so it's radius is 8/2= 4 inches

$area \: circle = \pi {r}^{2} = \pi \times {4}^{2} = 16\pi$
now we just subtract and our answer is

$64 - 16\pi = 64 - 16 \times (3.14) = 13.73$