2026 IGCSE Additional Mathematics May/June 0606/23 Q2

In this question lengths are in centimetres.

The diagram shows a shape \(ABCDP\).

\(AB\), \(BC\) and \(CD\) are three sides of a square.

The arc \(AD\) is part of a circle centre \(P\).

\(M\) is the midpoint of \(BC\).

\(AB=BC=CD=4\) and \(MP=5\).

Angle \(APD=\theta\) radians.

1. Show that \(\theta=2.21\) to 3 significant figures.[2]
2. Find the area of the shaded region.[5]