7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f8ece90a-5042-4db1-9855-ffe74333a899-4_542_625_959_589}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{figure}
Figure 2 shows a uniform lamina \(A B C D\) formed by removing an isosceles triangle \(B C D\) from an equilateral triangle \(A B D\) of side \(2 d\). The point \(C\) is the centroid of triangle \(A B D\).
- Find the area of triangle \(B C D\) in terms of \(d\).
- Show that the distance of the centre of mass of the lamina from \(B D\) is \(\frac { 4 } { 9 } \sqrt { 3 } d\).
(8 marks)
The lamina is freely suspended from the point \(B\) and hangs at rest. - Find in degrees, correct to 1 decimal place, the acute angle that the side \(A B\) makes with the vertical.