The area of the yellow regions is . What is the area of the blue rectangle?
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Let the radius of each circle be r and the area of the rectangle be 2 r ⋅ 4 r = 8 r 2 . Solving for r 2 using the given yellow area gives:
8 r 2 − 2 ( π r 2 ) = 3 2 − 8 π ⇒ r 2 = 4 .
Thus the rectangle's area computes to 8 ( 4 ) = 3 2 .