7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6f31b6f1-33b5-4bca-9030-cf93760b454d-09_432_656_210_644}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The triangle \(X Y Z\) in Figure 1 has \(X Y = 6 \mathrm {~cm} , Y Z = 9 \mathrm {~cm} , Z X = 4 \mathrm {~cm}\) and angle \(Z X Y = \alpha\). The point \(W\) lies on the line \(X Y\).
The circular arc \(Z W\), in Figure 1 is a major arc of the circle with centre \(X\) and radius 4 cm .
- Show that, to 3 significant figures, \(\alpha = 2.22\) radians.
- Find the area, in \(\mathrm { cm } ^ { 2 }\), of the major sector \(X Z W X\).
The region enclosed by the major arc \(Z W\) of the circle and the lines \(W Y\) and \(Y Z\) is shown shaded in Figure 1.
Calculate
- the area of this shaded region,
- the perimeter \(Z W Y Z\) of this shaded region.