Problem 9. The answer is (B).

The four regions in the figure all have the same area. Their union is formed by a central square with a side of 2, and thus an area of 4, and by four semicircles of radius 1, each with an area of $\pi / 2$. The total area is therefore $4+2 \pi$, while each of the four regions will have an area of $1+\pi / 2$.

(Problem proposed by R. Zanotto)
9. The figure on the side is formed by 4 congruent arcs of circles with radius 1. What is the area of the shaded region?
(A) $3-\pi / 4$
(D) $2+\pi / 4$
(B) $1+\pi / 2$
(C) $\pi-1 / 2$
(E) $4-\pi / 2$

![](https://cdn.mathpix.com/cropped/2024_04_17_82169a1997fb4f3442bcg-2.jpg?height=250&width=265&top_left_y=114&top_left_x=1076)