Edexcel C2 2014 June — Question 5

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2014
SessionJune
TopicRadians, Arc Length and Sector Area

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f07cc9ed-a820-46c8-a3a3-3c780cf20fa7-08_566_725_127_614} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows the shape \(A B C D E A\) which consists of a right-angled triangle \(B C D\) joined to a sector \(A B D E A\) of a circle with radius 7 cm and centre \(B\).
\(A , B\) and \(C\) lie on a straight line with \(A B = 7 \mathrm {~cm}\).
Given that the size of angle \(A B D\) is exactly 2.1 radians,
  1. find, in cm, the length of the arc \(D E A\),
  2. find, in cm, the perimeter of the shape \(A B C D E A\), giving your answer to 1 decimal place.