Edexcel C2 2009 January — Question 7

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2009
SessionJanuary
TopicRadians, Arc Length and Sector Area

7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{12e54724-64a3-4dc0-b7d5-6ef6cc04124c-09_878_991_233_461} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} The shape \(B C D\) shown in Figure 3 is a design for a logo. The straight lines \(D B\) and \(D C\) are equal in length. The curve \(B C\) is an arc of a circle with centre \(A\) and radius 6 cm . The size of \(\angle B A C\) is 2.2 radians and \(A D = 4 \mathrm {~cm}\). Find
  1. the area of the sector \(B A C\), in \(\mathrm { cm } ^ { 2 }\),
  2. the size of \(\angle D A C\), in radians to 3 significant figures,
  3. the complete area of the logo design, to the nearest \(\mathrm { cm } ^ { 2 }\).