(i) To find the area of the shaded region, we need to calculate the area of triangle OQR and subtract the area of sector OPQ.

The length QR is given by QR = r \tan \theta.

The area of triangle OQR is \(\frac{1}{2} \times r \times r \tan \theta = \frac{1}{2}r^2 \tan \theta\).

The area of sector OPQ is \(\frac{1}{2}r^2 \theta\).

Thus, the area of the shaded region is \(\frac{1}{2}r^2 \tan \theta - \frac{1}{2}r^2 \theta = \frac{1}{2}r^2(\tan \theta - \theta)\).

(ii) Given θ = 0.8 and r = 15, we calculate the perimeter of the shaded region.

The arc length PQ is \(r \theta = 15 \times 0.8 = 12 \text{ cm}\).

The length OR is \(\frac{r}{\cos \theta} = \frac{15}{\cos 0.8} \approx 21.53 \text{ cm}\).

The perimeter of the shaded region is \(r \tan \theta + \text{arc } PQ + (r - r \cos \theta)\).

Substituting the values, we get \(15 \tan 0.8 + 12 + (15 - 15 \cos 0.8) \approx 34.0 \text{ cm}\).