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UKMT Intermediate Mathematical Challenge, 2021

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

A semicircle is drawn on each side of a square, as shown. The square has sides of length $2\pi$ . What is the area of the resulting shape?

(A) $2\pi^2(\pi + 1)$ (B) $\pi^2(\pi + 2)$ (C) $2\pi^2(2\pi + 1)$ (D) $\pi^2(\pi + 4)$ (E) $2\pi^2(\pi + 2)$

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