5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7e2b7c81-e678-4078-964b-8b78e3b63f43-10_529_1403_255_267}
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\caption{Figure 2}
\end{figure}
Figure 2 shows the plan view of a garden.
The shape of the garden \(A B C D E A\) consists of a triangle \(A B E\) and a right-angled triangle \(B C D\) joined to a sector \(B D E\) of a circle with radius 6 m and centre \(B\).
The points \(A , B\) and \(C\) lie on a straight line with \(A B = 10.8 \mathrm {~m}\)
Angle \(B C D = \frac { \pi } { 2 }\) radians, angle \(E B D = 1.3\) radians and \(A E = 12.2 \mathrm {~m}\)
- Find the area of the sector \(B D E\), giving your answer in \(\mathrm { m } ^ { 2 }\)
- Find the size of angle \(A B E\), giving your answer in radians to 2 decimal places.
- Find the area of the garden, giving your answer in \(\mathrm { m } ^ { 2 }\) to 3 significant figures.