(i) The area of sector OAB is given by \(\frac{1}{2} \times 8^2 \times \alpha = 32\alpha\).

The area of semicircle OAC is \(\frac{1}{2} \times \pi \times 4^2 = 8\pi\).

According to the problem, \(8\pi = 2 \times 32\alpha\).

Solving for \(\alpha\), we get \(\alpha = \frac{\pi}{8}\).

(ii) The perimeter of the complete figure consists of the straight lines OA and OB, and the arcs AB and AC.

The length of OA and OB is 8 cm each.

The length of arc AB is \(8 \times \frac{\pi}{8} = \pi\).

The length of arc AC is \(\frac{1}{2} \times 8\pi = 4\pi\).

Thus, the total perimeter is \(8 + 8 + \pi + 4\pi = 8 + 5\pi\).