5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1e5324f5-a9bc-4041-bfbb-cb940417ea63-16_360_773_255_646}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a solid display stand with parallel triangular faces \(A B C\) and \(D E F\). Triangle \(D E F\) is similar to triangle \(A B C\).
With respect to a fixed origin \(O\), the points \(A , B\) and \(C\) have coordinates ( \(3 , - 3,1\) ), ( \(- 5,3,3\) ) and ( \(1,7,5\) ) respectively and the points \(D , E\) and \(F\) have coordinates ( \(2 , - 1,8\) ), ( \(- 2,2,9\) ) and ( \(1,4,10\) ) respectively. The units are in centimetres.
- Show that the area of the triangular face \(D E F\) is \(\frac { 1 } { 2 } \sqrt { 339 } \mathrm {~cm} ^ { 2 }\)
- Find, in \(\mathrm { cm } ^ { 3 }\), the exact volume of the display stand.