IKMC 2017 - Grades 11-12 - Self-study Question 22

Question 22

The diagram shows a regular hexagon with side length 1. The grey flower is outlined by circular arcs with radius 1 whose centres lie in the vertices of the hexagon. How big is the area of the grey flower?

Question illustration

$\frac\pi2$
$\frac{2\pi}3$
$2\sqrt3-\pi$
$\frac\pi2+\sqrt3$
$2\pi-3\sqrt3$