(i) To find the area of the shaded region, we calculate the area of the sector and subtract the area of triangle OCD.

The area of the sector is given by \(\frac{1}{2} r^2 \theta\), where \(r = 6 \text{ cm}\) and \(\theta = 0.8 \text{ radians}\). Thus, the area of the sector is \(\frac{1}{2} \times 6^2 \times 0.8 = 14.4 \text{ cm}^2\).

The area of triangle OCD is given by \(\frac{1}{2} ab \sin C\), where \(a = b = 10 \text{ cm}\) and \(C = 0.8 \text{ radians}\). Thus, the area of the triangle is \(\frac{1}{2} \times 10^2 \times \sin 0.8 = 35.9 \text{ cm}^2\).

The shaded area is \(14.4 - 35.9 = 21.5 \text{ cm}^2\).

(ii) To find the perimeter of the shaded region, we calculate the arc length and the length of CD.

The arc length is given by \(s = r \theta\), where \(r = 6 \text{ cm}\) and \(\theta = 0.8 \text{ radians}\). Thus, the arc length is \(6 \times 0.8 = 4.8 \text{ cm}\).

The length of CD can be found using the cosine rule or \(2 \times 10 \times \sin 0.4\). Thus, \(CD = 7.8 \text{ cm}\).

The perimeter of the shaded region is \(8 + 4.8 + 7.8 = 20.6 \text{ cm}\).