2024 IGCSE Additional Mathematics October/November 0606/21 Q6

In this question all lengths are in metres.

The diagram shows a shape \(ABCDEF\).

\(AB\), \(BD\) and \(DE\) are three sides of a rectangle.

\(O\) is the mid-point of \(BD\).

\(AFE\) is an arc of a circle whose centre is \(O\).

\(AB=\sqrt3\), \(BC=CD=5\) and \(BD=6\).

1. Find the exact value of the perimeter of the shape, giving your answer in terms of \(\pi\).[5]
2. Find the exact value of the area of the shape, giving your answer in terms of \(\pi\).[3]