9.
\begin{figure}[h]
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\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{872356ab-68d3-43ee-8b76-650a2697d80e-11_627_965_338_502}
\end{figure}
Figure 2 shows a plan of a patio. The patio \(P Q R S\) is in the shape of a sector of a circle with centre \(Q\) and radius 6 m .
Given that the length of the straight line \(P R\) is \(6 \sqrt { } 3 \mathrm {~m}\),
- find the exact size of angle \(P Q R\) in radians.
- Show that the area of the patio \(P Q R S\) is \(12 \pi \mathrm {~m} ^ { 2 }\).
- Find the exact area of the triangle \(P Q R\).
- Find, in \(\mathrm { m } ^ { 2 }\) to 1 decimal place, the area of the segment \(P R S\).
- Find, in \(m\) to 1 decimal place, the perimeter of the patio \(P Q R S\).