The green, leaf-shaped area below is the region of overlap between two circles of radius \large 2 that are centered, respectively, at the two opposite corners of the \large 2 \times 2  square. What is the area of this green region?


Correct Answer: \large 2\pi -4

Cut the leaf along the square's diagonal, and rotate the bottom section as follows:


Now the green region is the difference between the semi-circle with a radius of \large 2 and a triangle with a base of  and a height of \large 2  which makes the area 

\large A=\frac{1}{2} \pi2^2-\frac{1}{2}\times 4\times 2 =2\pi -4

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