15.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{1528bec3-7a7a-42c5-bac2-756ff3493818-36_394_608_287_676}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}

The triangle $X Y Z$ in Figure 4 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 4 is a major arc of the circle with centre $X$ and radius 4 cm .
\begin{enumerate}[label=(\alph*)]
\item Show that, to 3 significant figures, $\alpha = 2.22$ radians.
\item 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 4.

Calculate
\item the area of this shaded region,
\item the perimeter $Z W Y Z$ of this shaded region.\\

\includegraphics[max width=\textwidth, alt={}, center]{1528bec3-7a7a-42c5-bac2-756ff3493818-39_90_54_2576_1868}
\end{enumerate}

\hfill \mbox{\textit{Edexcel C12  Q15 [12]}}