8.
\section*{Diagram NOT to scale}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{db979349-3415-420f-a39f-8cc8c24a69d0-20_461_1036_296_534}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows the plan view of a design for a pond.
The design consists of a sector \(A O B X\) of a circle centre \(O\) joined to a quadrilateral \(A O B C\).
- \(B C = 8 \mathrm {~m}\)
- \(O A = O B = 3 \mathrm {~m}\)
- angle \(A O B\) is \(\frac { 2 \pi } { 3 }\) radians
- angle \(B C A\) is \(\frac { \pi } { 6 }\) radians
- Calculate (i) the exact area of the sector \(A O B X\),
(ii) the exact perimeter of the sector \(A O B X\). - Calculate the exact area of the triangle \(A O B\).
- Show that the length \(A B\) is \(3 \sqrt { 3 } \mathrm {~m}\).
- Find the total surface area of the pond. Give your answer in \(\mathrm { m } ^ { 2 }\) correct to 2 significant figures.