3.48: Concentric arcs: shaded area and perimeter

In the diagram, $AD$ and $BC$ are arcs of circles with common centre $O$. $ODC$ and $OAB$ are straight lines with $OA = 5\text{ cm}$ and $AB = 4\text{ cm}$. Angle $BOC = \theta$ radians. The area of the shaded region $ABCD$ is $4\pi\text{ cm}^{2}$.