SOLUTION: Find the area of one segment formed by a square with sides of 6" inscribed in a circle.

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Question 461955: Find the area of one segment formed by a square with sides of 6" inscribed in a circle.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The diagonal of the square is 6sqrt%282%29 inches, since an edge is 6 inches long. The radius of the circle is then half of this, or 3sqrt%282%29 inches. Hence the area of the circle is A+=+%283sqrt%282%29%29%5E2%2Api+=+18pi square inches. The area of the square is 36 square inches.
The area of one segment, by symmetry, is a quarter of the difference between the area of the circle and the area of the inscribed square, or
%2818pi+-+36%29%2F4+=+%289pi+-+18%29%2F2 square inches.