B2. Given is a square $A B C D$ with side lengths of 4. Inside the square, two semicircles with diameters $A B$ and $B C$ are drawn (see figure).

What is the combined area of the two gray regions?

![](https://cdn.mathpix.com/cropped/2024_04_17_a2fe9fdc1344cf064d71g-1.jpg?height=308&width=314&top_left_y=1322&top_left_x=1545)
B2. 8 Note that both circles pass through the center of the square. The four circular segments marked with $p, q, r$ and $s$ therefore all belong to a quarter of a circle with radius 2 and thus have the same area. The total area of the gray region is therefore equal to the area of triangle $A C D$ and thus equal to $\frac{1}{2} \cdot 4 \cdot 4=8$.

![](https://cdn.mathpix.com/cropped/2024_04_17_ed08a24c376b53c33fffg-1.jpg?height=311&width=311&top_left_y=1278&top_left_x=1569)