4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a7ef3811-3594-4ecd-a616-36f42d26489b-06_428_803_233_577}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of the curve with polar equation
$$r = a + 3 \cos \theta , \quad a > 0 , \quad 0 \leqslant \theta < 2 \pi$$
The area enclosed by the curve is \(\frac { 107 } { 2 } \pi\).
Find the value of \(a\).