3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{47420c50-c232-41e9-8c4d-a890d86ea933-04_814_1127_219_411}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The uniform lamina \(A B C D E F\), shown shaded in Figure 1, is symmetrical about the line through \(B\) and \(E\). It is formed by removing the isosceles triangle \(F E D\), of height \(6 a\) and base \(8 a\), from the isosceles triangle \(A B C\) of height \(9 a\) and base \(12 a\).
- Find, in terms of \(a\), the distance of the centre of mass of the lamina from \(A C\).
The lamina is freely suspended from \(A\) and hangs in equilibrium.
- Find, to the nearest degree, the size of the angle between \(A B\) and the downward vertical.