Each side of the square measures units. Find the area of the blue circle. Give your answer to the nearest integer.
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Let the square be A B C D and the center of the blue circle be O . Due to symmetry, the circle touch the base of A B C D at the midpoint M or C D . By Pythagorean theorem , we have:
O M 2 + D M 2 r 2 + 2 2 8 r ⟹ r = O D 2 = ( 4 − r ) 2 = r 2 − 8 r + 1 6 = 1 2 = 8 1 2 = 2 3
Then the area of the blue circle is ( 2 3 ) 2 π ≈ 7 .