Edexcel C12 2019 January — Question 10

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
Year2019
SessionJanuary
TopicRadians, Arc Length and Sector Area

10. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{75d68987-2314-4c8f-8160-24977c5c4e34-20_761_1475_331_239} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows the design for a shop sign \(A B C D A\). The sign consists of a triangle \(A O D\) joined to a sector of a circle \(D O B C D\) with radius 1.8 m and centre \(O\). The points \(A , B\) and \(O\) lie on a straight line.
Given that \(A D = 3.9 \mathrm {~m}\) and angle \(B O D\) is 0.84 radians,
  1. calculate the size of angle \(D A O\), giving your answer in radians to 3 decimal places.
  2. Show that, to one decimal place, the length of \(A O\) is 4.9 m .
  3. Find, in \(\mathrm { m } ^ { 2 }\), the area of the shop sign, giving your answer to one decimal place.
  4. Find, in m , the perimeter of the shop sign, giving your answer to one decimal place.