1.58: Arc Length and Sector Area

Figure 1 shows sector $\displaystyle AOB$ of a circle with centre $\displaystyle O$ and radius $\displaystyle r\,\mathrm{cm}$. The angle $\displaystyle AOB$ is 1.5 radians and the length of arc $\displaystyle AB$ is $\displaystyle 12\,\mathrm{cm}$.

Calculate

(a) the value of $\displaystyle r$,

(b) the area of the sector $\displaystyle AOB$.