1.49: Past-paper question 3

Figure 1 shows sector $\displaystyle OABC$ of a circle with centre $\displaystyle O$ and radius 6 cm

The size of angle $\displaystyle AOC$ is $\displaystyle \theta$ radians.

The perimeter of sector $\displaystyle OABC$ is $\displaystyle (12 + \pi)$ cm

The region shown shaded in Figure 1 is bounded by the arc $\displaystyle ABC$ and the line $\displaystyle AC$

The area of this region is $\displaystyle S \mathrm{cm}^2$

Find the exact value of $\displaystyle S$