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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