4.04: Arc geometry and area

0606/23/M/J/26 — Question 2 · 7 marks

\(AB\), \(BC\) and \(CD\) are sides of a square of side \(4\). \(AD\) is an arc of a circle with centre \(P\). \(M\) is the midpoint of \(BC\), \(MP=5\), and \(\angle APD=\theta\).
(a)
Show that \(\theta=2.21\) correct to \(3\) significant figures.
[2]
(b)
Find the shaded area.
[5]
Official diagram for Question 2