When a square is circumscribed by a circle , the diagonal of the square is equal to the diameter of the circle.
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 .
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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