three circles in a rectangle

Geometry Level 1

The area of the yellow regions is 32 8 π 32-8\pi . What is the area of the blue rectangle?


The answer is 32.

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1 solution

Tom Engelsman
Jun 23, 2019

Let the radius of each circle be r r and the area of the rectangle be 2 r 4 r = 8 r 2 2r \cdot 4r = 8r^2 . Solving for r 2 r^2 using the given yellow area gives:

8 r 2 2 ( π r 2 ) = 32 8 π r 2 = 4. 8r^2 - 2(\pi r^2) = 32-8\pi \Rightarrow r^2 = 4.

Thus the rectangle's area computes to 8 ( 4 ) = 32 . 8(4) = \boxed{32}.

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