8) What is the area of the region delimited by the four semicircles with a diameter of $10 \mathrm{~cm}$ shown in the figure?
(A) $100 \mathrm{~cm}^{2}$
(D) $100 \pi \mathrm{cm}^{2}$
(B) $100 \pi \sqrt{2} \mathrm{~cm}^{2}$
(C) $50 \pi \mathrm{cm}^{2}$
(E) $25 \pi \mathrm{cm}^{2}$

![](https://cdn.mathpix.com/cropped/2024_04_17_548b825896d130d6fc47g-1.jpg?height=183&width=354&top_left_y=826&top_left_x=2415)
8) The answer is (A)

By decomposing the given figure along the dashed lines and recomposing it by rotating the two semicircles $270^{\circ}$ clockwise around $A$ and $B$ respectively (see figures below), a square with a side length of $10 \mathrm{~cm}$ is obtained. The area of this square, which is equivalent to the area of the given figure, is $100 \mathrm{~cm}^{2}$.
![](https://cdn.mathpix.com/cropped/2024_04_17_e738d1c220e6fc403f5eg-2.jpg?height=330&width=1326&top_left_y=454&top_left_x=388)