8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0839eb5f-2850-4d77-baf7-a6557d71076e-18_505_1301_257_572}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows the plan view of a stage.
The plan view shows two congruent triangles \(A B O\) and \(G F O\) joined to a sector \(O C D E O\) of a circle, centre \(O\), where
- angle \(C O E = 2.3\) radians
- arc length \(C D E = 27.6 \mathrm {~m}\)
- \(A O G\) is a straight line of length 15 m
- Show that \(O C = 12 \mathrm {~m}\).
- Show that the size of angle \(A O B\) is 0.421 radians correct to 3 decimal places.
Given that the total length of the front of the stage, \(B C D E F\), is 35 m ,
find the total area of the stage, giving your answer to the nearest square metre.