A2. In a square with side 2, we draw two semicircles, whose diameters are the sides of the square, as shown in the figure. What is the area of the unshaded part of the square?
(A) $\frac{\pi}{2}$
(B) 2
(C) $\frac{3}{2}+\frac{\pi}{4}$
(D) $\frac{3 \pi}{4}-\frac{1}{2}$
(E) $\frac{3 \pi}{4}$

![](https://cdn.mathpix.com/cropped/2024_06_07_6340f9febbabfa1859cdg-10.jpg?height=226&width=217&top_left_y=1018&top_left_x=1685)
A2. If we draw both diagonals on the sketch, we observe that the triangles $A, B, C$ and $D$ have equal areas. The area of the unshaded part of the square is therefore equal to half the area of the square, which is $\frac{4}{2}=2$. The correct answer is $B$.

![](https://cdn.mathpix.com/cropped/2024_06_07_6340f9febbabfa1859cdg-23.jpg?height=217&width=214&top_left_y=1151&top_left_x=1635)