7.
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{de11ae90-8693-4346-b195-1d01f2b164f5-02_446_688_251_1745}
\end{figure}
Figure 1 shows the triangle \(A B C\), with \(A B = 8 \mathrm {~cm} , A C = 11 \mathrm {~cm}\) and \(\angle B A C = 0.7\) radians. The \(\operatorname { arc } B D\), where \(D\) lies on \(A C\), is an arc of a circle with centre \(A\) and radius 8 cm . The region \(R\), shown shaded in Figure 1, is bounded by the straight lines \(B C\) and \(C D\) and the \(\operatorname { arc } B D\).
Find
- the length of the arc \(B D\),
- the perimeter of \(R\), giving your answer to 3 significant figures,
- the area of \(R\), giving your answer to 3 significant figures.