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\includegraphics[max width=\textwidth, alt={}, center]{56d376c5-b91f-488d-89e2-18edcb14052d-2_512_903_1302_621} The diagram represents a metal plate \(O A B C\), consisting of a sector \(O A B\) of a circle with centre \(O\) and radius \(r\), together with a triangle \(O C B\) which is right-angled at \(C\). Angle \(A O B = \theta\) radians and \(O C\) is perpendicular to \(O A\).

1. Find an expression in terms of \(r\) and \(\theta\) for the perimeter of the plate.
2. For the case where \(r = 10\) and \(\theta = \frac { 1 } { 5 } \pi\), find the area of the plate.