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.

(i) Find an expression in terms of r and \(\theta\) for the perimeter of the plate.

(ii) For the case where r = 10 and \(\theta = \frac{1}{5}\pi\), find the area of the plate.