4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{752efc6c-8d0e-46a6-b75d-5125956969d8-10_508_960_212_477}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Diagram not drawn to scale
Figure 1 is a sketch representing the cross-section of a large tent \(A B C D E F\). \(A B\) and \(D E\) are line segments of equal length.
Angle \(F A B\) and angle \(D E F\) are equal.
\(F\) is the midpoint of the straight line \(A E\) and \(F C\) is perpendicular to \(A E\).
\(B C D\) is an arc of a circle of radius 3.5 m with centre at \(F\).
It is given that
$$\begin{aligned}
A F & = F E = 3.7 \mathrm {~m}
B F & = F D = 3.5 \mathrm {~m}
\text { angle } B F D & = 1.77 \text { radians }
\end{aligned}$$
Find
- the length of the arc \(B C D\) in metres to 2 decimal places,
- the area of the sector \(F B C D\) in \(\mathrm { m } ^ { 2 }\) to 2 decimal places,
- the total area of the cross-section of the tent in \(\mathrm { m } ^ { 2 }\) to 2 decimal places.