(i) The perimeter of the shaded region ABDC is given by the sum of the lengths of arcs AB and CD, and the radii OA and OB. The length of arc AB is \(2r\alpha\) and the length of arc CD is \(r\alpha\). Therefore, the perimeter is:

\(2r\alpha + r\alpha + 2r = 4.4r\)

Simplifying, we get:

\(3r\alpha + 2r = 4.4r\)

\(3r\alpha = 2.4r\)

\(\alpha = 0.8\)

(ii) The area of the shaded region is the difference between the area of sector OAB and sector OCD. The area of sector OAB is \(\frac{1}{2}(2r)^2\alpha\) and the area of sector OCD is \(\frac{1}{2}r^2\alpha\). Therefore, the area of the shaded region is:

\(\frac{1}{2}(2r)^2 \times 0.8 - \frac{1}{2}r^2 \times 0.8 = 30\)

\(2r^2 \times 0.8 - 0.5r^2 \times 0.8 = 30\)

\((3/2)r^2 \times 0.8 = 30\)

\(r^2 \times 1.2 = 30\)

\(r^2 = 25\)

\(r = 5\)