6 A sector of a circle has radius \(r \mathrm {~cm}\) and sector angle \(\theta\) radians. It is divided into two regions, A and B . Region A is an isosceles triangle with the equal sides being of length \(a \mathrm {~cm}\), as shown in Fig. 6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{50ebbd77-39da-4a48-993a-bcf99ada9dcd-3_407_469_1343_612}
\captionsetup{labelformat=empty}
\caption{Fig. 6}
\end{figure}
\section*{Not to scale}
- Express the area of B in terms of \(a , r\) and \(\theta\).
- Given that \(r = 12\) and \(\theta = 0.8\), find the value of \(a\) for which the areas of A and B are equal. Give your answer correct to 3 significant figures.