11.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{aa75f1c1-ee97-4fee-af98-957e6a3fbba1-16_892_825_228_548}
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\caption{Figure 2}
\end{figure}
Diagram not drawn to scale
Figure 2 shows the design for a sail \(A P B C A\).
The curved edge \(A P B\) of the sail is an arc of a circle centre \(O\) and radius \(r \mathrm {~m}\).
The straight edge \(A C B\) is a chord of the circle.
The height \(A B\) of the sail is 2.4 m .
The maximum width \(C P\) of the sail is 0.4 m .
- Show that \(r = 2\)
- Show, to 4 decimal places, that angle \(A O B = 1.2870\) radians.
- Hence calculate the area of the sail, giving your answer, in \(\mathrm { m } ^ { 2 }\), to 3 decimal places.