Edexcel C2 2013 June — Question 5

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2013
SessionJune
TopicRadians, Arc Length and Sector Area

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1c51b071-5cb1-4841-b031-80bde9027433-08_598_1297_118_319} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows a plan view of a garden.
The plan of the garden \(A B C D E A\) consists of a triangle \(A B E\) joined to a sector \(B C D E\) of a circle with radius 12 m and centre \(B\).
The points \(A , B\) and \(C\) lie on a straight line with \(A B = 23 \mathrm {~m}\) and \(B C = 12 \mathrm {~m}\).
Given that the size of angle \(A B E\) is exactly 0.64 radians, find
  1. the area of the garden, giving your answer in \(\mathrm { m } ^ { 2 }\), to 1 decimal place,
  2. the perimeter of the garden, giving your answer in metres, to 1 decimal place.