2 The diagram shows a sector \(O A B\) of a circle with centre \(O\).
\includegraphics[max width=\textwidth, alt={}, center]{258f0400-6e3b-406c-9f86-acc9fff4e094-2_440_392_1500_826}
The radius of the circle is 6 cm and the angle \(A O B = 0.5\) radians.
- Find the area of the sector \(O A B\).
- Find the length of the arc \(A B\).
- Hence show that the perimeter of the sector \(O A B = k \times\) the length of the \(\operatorname { arc } A B\) where \(k\) is an integer.