MathNet 2021 — Part 01 Question 10

Question 10

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?

$\frac{5\sqrt{3}}{2} - \pi$
$3\sqrt{3} - \pi$
$4\sqrt{3} - \frac{3\pi}{2}$
$\pi - \frac{\sqrt{3}}{2}$
$\frac{\pi + \sqrt{3}}{2}$