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\includegraphics[max width=\textwidth, alt={}, center]{b6ae63ce-a8a8-45ef-9c75-2fab30de8ad9-3_408_451_721_845}
In the diagram, \(A O B\) is a quarter circle with centre \(O\) and radius \(r\). The point \(C\) lies on the arc \(A B\) and the point \(D\) lies on \(O B\). The line \(C D\) is parallel to \(A O\) and angle \(A O C = \theta\) radians.
- Express the perimeter of the shaded region in terms of \(r , \theta\) and \(\pi\).
- For the case where \(r = 5 \mathrm {~cm}\) and \(\theta = 0.6\), find the area of the shaded region.