The area of a sector of a circle with radius \(r\) and central angle \(\theta\) is
\(A=\dfrac{r^2}2\theta\)
which comes from the proportion relation,
\(\dfrac{\text{area of circle}}{\text{one full revolution}}=\dfrac{\pi r^2}{2\pi}=\dfrac A\theta=\dfrac{\text{area of sector}}{\text{measure of central angle (radians)}}\)
You have \(30^\circ=\dfrac\pi6\text{ rad}\), so the area is
\(A=\dfrac{6^2}2\times\dfrac\pi6=3\pi\)
