(i) The area of the shaded region is the difference between the areas of sectors OAB and OCD.

The area of sector OAB is \(\frac{1}{2} \times 16^2 \times 0.8\).

The area of sector OCD is \(\frac{1}{2} \times 10^2 \times 0.8\).

Thus, the area of the shaded region is \(\frac{1}{2} \times 16^2 \times 0.8 - \frac{1}{2} \times 10^2 \times 0.8 = 62.4 \text{ cm}^2\).

(ii) The perimeter of the shaded region consists of the arcs AC and BD and the straight lines AB and CD.

The length of arc AC is \(10 \alpha\) and the length of arc BD is \(16 \alpha\).

The lengths of AB and CD are both 6 cm.

Thus, the perimeter is \(10 \alpha + 16 \alpha + 6 + 6 = 28.9\).

Solving \(26 \alpha + 12 = 28.9\) gives \(\alpha = 0.65\).