When a square is circumscribed by a circle , the diagonal of the square is equal to the diameter of the circle.
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 2 times the length of a side. Therefore: s 2 = 3 s = 3 2 = 3 2 2 in .
Example 2: Find the area of the circle.
First, find the diagonal of the square. Its length is 2 times the length of the side, or 5 2 cm. This value is also the diameter of the circle. So, the radius of the circle is half that length, or 5 2 2 . To find the area of the circle, use the formula A = π r 2 . A = π ( 5 2 2 ) 2 = π ( 25 ⋅ 2 4 ) = 25 2 π cm 2 |