7.
\section*{Figure 2}
\includegraphics[max width=\textwidth, alt={}]{8c2ee205-d02f-413d-abf7-e259c0734353-3_558_642_605_651}
Fig. 2 shows the sector \(O A B\) of a circle of radius \(r \mathrm {~cm}\). The area of the sector is \(15 \mathrm {~cm} ^ { 2 }\) and \(\angle A O B = 1.5\) radians.
- Prove that \(r = 2 \sqrt { 5 }\).
- Find, in cm , the perimeter of the sector \(O A B\).
The segment \(R\), shaded in Fig 1, is enclosed by the arc \(A B\) and the straight line \(A B\).
- Calculate, to 3 decimal places, the area of \(R\).