Circles Inscribed in Squares

When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square.

Example 1:

Find the side length s of the square.

The diagonal of the square is 3 inches. We know from the Pythagorean Theorem that the diagonal of a square is times the length of a side. Therefore:

Example 2:

Find the area of the circle.

First, find the diagonal of the square. Its length is times the length of the side, or cm.

This value is also the diameter of the circle. So, the radius of the circle is half that length, or .

To find the area of the circle, use the formula .