IP2U13 13.4 PN1 Q8

The diagram shows a sector of a circle with centre \(O\) and radius \(8\) cm.

\(P\) is a point on \(OA\) such that \(4OP = 3OA\) and \(Q\) is a point on \(OB\) such that \(5OQ = 2OB\).

Given that \(\angle AOB = 0.8\) radians, calculate

1. the length of \(PQ\),
2. the arc length \(AB\),
3. the area of the shaded region.