10.334. Inside a square with side $a$, a semicircle is constructed on each side as a diameter. Find the area of the rosette bounded by the arcs of the semicircles.
## Solution.

Chord $O A$ subtends an arc of $90^{\circ}$ (Fig. 10.120); therefore, the area of half a petal is $\frac{\pi a^{2}}{16}-\frac{a^{2}}{8}=\frac{a^{2}(\pi-2)}{16}$.

From this, the desired area $S=8 \cdot \frac{a^{2}(\pi-2)}{16}=\frac{a^{2}(\pi-2)}{2}$.

Answer: $\frac{a^{2}(\pi-2)}{2}$.