11.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{88ed9a17-97a5-4548-80bb-70b4b901a39d-13_625_1155_285_456}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a triangle \(X Y Z\) with \(X Y = 10 \mathrm {~cm} , Y Z = 16 \mathrm {~cm}\) and \(Z X = 12 \mathrm {~cm}\).
- Find the size of the angle \(Y X Z\), giving your answer in radians to 3 significant figures.
The point \(A\) lies on the line \(X Y\) and the point \(B\) lies on the line \(X Z\) and \(A X = B X = 5 \mathrm {~cm} . A B\) is the arc of a circle with centre \(X\).
The shaded region \(S\), shown in Figure 1, is bounded by the lines \(B Z , Z Y , Y A\) and the arc \(A B\).
Find
- the perimeter of the shaded region to 3 significant figures,
- the area of the shaded region to 3 significant figures.