5. Let $A B C D E F$ be a regular hexagon with side length 2 . A circle with radius 3 and center at $A$ is drawn. Find the area inside quadrilateral $B C D E$ but outside the circle.
Answer: $4 \sqrt{3}-\frac{3}{2} \pi$
Solution: Rotate the region 6 times about $A$ to form a bigger hexagon with a circular hole. The larger hexagon has side length 4 and area $24 \sqrt{3}$, so the area of the region is $\frac{1}{6}(24 \sqrt{3}-9 \pi)=4 \sqrt{3}-\frac{3}{2} \pi$.