The diagram shows a metal plate OABCDEF consisting of 3 sectors, each with centre O. The radius of sector COD is 2r and angle COD is θ radians. The radius of each of the sectors BOA and FOE is r, and AOED and CBOF are straight lines.

(i) Show that the area of the metal plate is r^2(π + θ).

(ii) Show that the perimeter of the metal plate is independent of θ.