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 size 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 size of the side, or 5 2 cm.

This value is likewise the diameter of the circle. So, the radius of the circle is half that length, or 5 2 2 .

To find the location of the circle, usage the formula A = π r 2 .

A = π ( 5 2 2 ) 2 = π ( 25 ⋅ 2 4 ) = 25 2 π     cm 2

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