2023 May TZ2 P1 Q1

The following diagram shows a circle with centre \(\mathrm{O}\) and radius \(4\) cm.

The points \(\mathrm{P}, \mathrm{Q}\) and \(\mathrm{R}\) lie on the circumference of the circle and \(\mathrm{P\hat{O}R} = \theta \), where \(\theta\) is measured in radians.
The length of arc \(\mathrm{PQR}\) is \(10\) cm.

1. Find the perimeter of the shaded sector.

   [2]

2. Find \(\theta\).

   [2]

3. Find the area of the shaded sector.

   [2]