2025 IGCSE Additional Mathematics October/November 0606/22 Q2

The diagram shows the shaded region \(ABCD\).

The lines \(AC\) and \(BD\) each have a length of 12 cm.

The lines \(AC\) and \(BD\) bisect each other at the point \(O\).

The lines \(AD\) and \(BC\) are parallel and each have a length of 4 cm.

The arcs \(AB\) and \(DC\) are part of a circle centre \(O\).

1. Find the obtuse angle \(AOB\).
   Give your answer in radians.[3]
   Use your answer to part (a) to find
2. 1. the perimeter of the shaded region[2]
   2. the area of the shaded region.[3]