Question

Area of the shaded segment=

Answer 1

The area of the entire sector is $(\pi)(6^{2}) \left(\frac{60}{360} \right)=6\pi$

The area of the triangle OAB is $\frac{\sqrt{3}}{4}(6^{2})=9\sqrt{3}$.

So, the area of the segment is $\boxed{6\pi-9\sqrt{3}}$