imc

The area of the hexagon is equal to $\frac{3(6{)}^2\sqrt{3}}{2}=54\sqrt{3}$ by the formula for the area of a hexagon. We note that each interior angle of the regular hexagon is $120^{\circ }$ which means that each sector is $\frac{1}{3}$ of the circle it belongs to. The area of each sector is $\frac{9\pi }{3}=3\pi$. The area of all six is $6\times 3\pi =18\pi$. The shaded area is equal to the area of the hexagon minus the sum of the area of all the sectors, which is equal to $\boxed{54\sqrt{3}-18\pi }$