5.
\begin{figure}[h]
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\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{afaf76d8-2a1f-4239-8275-70fad4f418c1-1_351_663_1529_693}
\end{figure}
The shaded area in Fig. 1 shows a badge \(A B C\), where \(A B\) and \(A C\) are straight lines, with \(A B = A C = 8 \mathrm {~mm}\). The curve \(B C\) is an arc of a circle, centre \(O\), where \(O B = O C =\) 8 mm and \(O\) is in the same plane as \(A B C\). The angle \(B A C\) is 0.9 radians.
- Find the perimeter of the badge.
- Find the area of the badge.