Question 11A regular hexagon of side length $1$ is inscribed in a circle. Each minor arc of the circle determined by a side of the hexagon is reflected over that side. What is the area of the region bounded by these $6$ reflected arcs?$ \frac{5\sqrt{3}}{2} - \pi $$ 3\sqrt{3}-\pi $$ 4\sqrt{3}-\frac{3\pi}{2} $$ \pi - \frac{\sqrt{3}}{2} $$ \frac{\pi + \sqrt{3}}{2} $