8
\includegraphics[max width=\textwidth, alt={}, center]{6bcc553c-4938-46ef-bba4-97391b4d58d4-10_348_700_262_721}
In the diagram, \(A B C\) is an isosceles triangle with \(A B = B C = r \mathrm {~cm}\) and angle \(B A C = \theta\) radians. The point \(D\) lies on \(A C\) and \(A B D\) is a sector of a circle with centre \(A\).
- Express the area of the shaded region in terms of \(r\) and \(\theta\).
- In the case where \(r = 10\) and \(\theta = 0.6\), find the perimeter of the shaded region.