3) The perimeter of the region depicted alongside is formed by four semicircles with a diameter of $10 \mathrm{~cm}$. What is its area?
(A) $100 \mathrm{~cm}^{2}$
(B) $100 \pi \sqrt{2} \mathrm{~cm}^{2}$
(C) $50 \pi \mathrm{~cm}^{2}$
(D) $100 \pi \mathrm{~cm}^{2}$
(E) $25 \pi \mathrm{~cm}^{2}$.

![](https://cdn.mathpix.com/cropped/2024_04_17_ad8c4c2d860e923409d8g-1.jpg?height=206&width=373&top_left_y=1553&top_left_x=1093)
3) 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_855938a0fb7ccfca2bc5g-1.jpg?height=344&width=1334&top_left_y=1518&top_left_x=384)