(i) The area of sector OCD is given by \(\frac{1}{2} (2r)^2 \theta = 2r^2 \theta\).

The area of sectors OAB and OEF is \(2 \times \frac{1}{2} r^2 (\pi - \theta) = r^2 (\pi - \theta)\).

Thus, the total area of the metal plate is \(2r^2 \theta + r^2 (\pi - \theta) = r^2 (\pi + \theta)\).

(ii) The arc length CD is \(2r \theta\).

The arc lengths AB and EF are \(2 \times r (\pi - \theta) = 2r (\pi - \theta)\).

The straight edges AO, OE, BO, and OF sum to \(4r\).

Thus, the total perimeter is \(2r \theta + 2r (\pi - \theta) + 4r = 2\pi r + 4r\), which is independent of \(\theta\).