2025 Nov TZ1 P2 Q1

The following diagram shows a regular polygon inscribed in a circle with centre \(O\) and radius \(r\) cm.
The angle \(\mathrm{A\hat{O}B}\) is \(\theta\), where \(\theta\) is measured in radians,
The arc \(\mathrm{AB}\) is \(12\) cm.

1. Find

   [3]

   1. \(\theta\);

   2. \(r\).

2. Find the area of the shaded region.

   [3]