The diagram shows a circle with radius r cm and centre O. Points A and B lie on the circle and ABCD is a rectangle. Angle AOB = 2θ radians and AD = r cm.

(i) Express the perimeter of the shaded region in terms of r and θ.

(ii) In the case where r = 5 and θ = \(\frac{1}{6} \pi\), find the area of the shaded region.