SPS SPS SM 2020 June — Question 2

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2020
SessionJune
TopicSine and Cosine Rules

2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f2033889-3cc5-48de-9bdb-cb1861921a2a-04_556_1052_1119_552} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Diagram not drawn to scale Figure 1 shows the plan view of a design for a stage at a concert.
The stage is modelled as a sector \(B C D F\), of a circle centre \(F\), joined to two congruent triangles \(A B F\) and \(E D F\). Given that
\(A F E\) is a straight line $$\begin{aligned} & A F = F E = 10.7 \mathrm {~m}
& B F = F D = 9.2 \mathrm {~m} \end{aligned}$$ angle \(B F D = 1.82\) radians
find
  1. the perimeter of the stage, in metres, to one decimal place,
  2. the area of the stage, in \(\mathrm { m } ^ { 2 }\), to one decimal place.