AMC 10 2021-fall-b Problem 11

A 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? $(\textbf{A})\: \frac{5\sqrt{3}}{2} - \pi (\textbf{B}) \: 3\sqrt{3}-\pi (\textbf{C}) \: 4\sqrt{3}-\frac{3\pi}{2} (\textbf{D}) \: \pi - \frac{\sqrt{3}}{2} (\textbf{E}) \: \frac{\pi + \sqrt{3}}{2}$