10.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ce06b37a-aa57-4256-bec8-7277c8a9fc65-24_348_593_221_534}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Diagram not drawn to scale
Figure 1 shows a semicircle with centre \(O\) and radius \(3 \mathrm {~cm} . X Y\) is the diameter of this semicircle. The point Z is on the circumference such that angle \(X O Z = 1.3\) radians. The shaded region enclosed by the chord \(X Z\), the arc \(Z Y\) and the diameter \(X Y\) is a template for a badge.
Find, giving each answer to 3 significant figures,
- the length of the chord \(X Z\),
- the perimeter of the template \(X Z Y X\),
- the area of the template.