14. The figure on the side is formed by 4 congruent arcs of circles with radius 2. What is the area of the shaded region?
(A) $8+\pi$
(B) $8+\pi / 2$
(C) $9+\pi / 4$
(D) $16-2 \pi$
(E) $4+2 \pi$

![](https://cdn.mathpix.com/cropped/2024_04_17_ccb981cb4d80b90fdff2g-2.jpg?height=254&width=250&top_left_y=1391&top_left_x=1091)
Problem 14. The answer is $\mathbf{( E )}$.

The four regions in the figure all have the same area. Their union is formed by a central square with a side of 4, and thus an area of 16, and by four semicircles of radius 2, each with an area of $(4 \pi) / 2=2 \pi$. The total area is therefore $16+8 \pi$, while each of the four regions will have an area of $4+2 \pi$.

(Problem proposed by R. Zanotto)