4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6b9c61ac-23ec-4346-933f-cf00a2e63695-08_435_807_285_630}
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\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of a solid doorstop made of wood. The doorstop is modelled as a tetrahedron.
Relative to a fixed origin \(O\), the vertices of the tetrahedron are \(A ( 2,1,4 )\), \(B ( 6,1,2 ) , C ( 4,10,3 )\) and \(D ( 5,8 , d )\), where \(d\) is a positive constant and the units are in centimetres.
- Find the area of the triangle \(A B C\).
Given that the volume of the doorstop is \(21 \mathrm {~cm} ^ { 3 }\)
- find the value of the constant \(d\).