6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bb21001f-fe68-4776-992d-ede1aae233d7-12_438_816_246_621}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Diagram NOT accurately drawn
Figure 1 shows the plan view for the design of a stage.
The design consists of a sector \(O B C\) of a circle, with centre \(O\), joined to two congruent triangles \(O A B\) and \(O D C\).
Given that
- angle \(B O C = 2.4\) radians
- area of sector \(B O C = 40 \mathrm {~m} ^ { 2 }\)
- \(A O D\) is a straight line of length 12.5 m
- find the radius of the sector, giving your answer, in m , to 2 decimal places,
- find the size of angle \(A O B\), in radians, to 2 decimal places.
Hence find
the total area of the stage, giving your answer, in \(\mathrm { m } ^ { 2 }\), to one decimal place,the total perimeter of the stage, giving your answer, in m , to one decimal place.