The diagram represents a metal plate $OABC$, consisting of a sector $OAB$ of a circle with centre $O$ and radius $r$, together with a triangle $OCB$ which is right-angled at $C$. Angle $AOB = \theta $ radians and $OC$ is perpendicular to $OA$.
a) Find an expression in terms of $r$ and $\theta $ for the perimeter of the plate.
b) For the case where $r = 10$ and $\theta = \frac{1}{5}\pi $, find the area of the plate.

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