Question

Each side of a square is 4 inches. Four circles of equal area are inscribed (constructed inside the square). Find the exact area of the region around the circles. (inside the square but outside the circles)

Answer 1

In order to find the area of the area outside the circles and inside the square, you need the area of the square minus the area of all the circles.

I assume you know the area of the square (s^2= 4^2 = 16 square inches). But the area of the circles is tricky.

The area of a circle is pi times r squared
$\pi \times r ^{2}$
So you need the radius. Knowing the side length is four inches and that two circles span one side length (as in the picture), you can divide the side length by two to get the diameter of one circle. Then divide that by two again to get the radius. Ultimately the radius is one.

The area using the circle area equation is ultimately just pi. However, with four circles you need to multiply this by four to get four pi.

So, 16-4pi is approximately 3.44 inches squared is the answer.