(i) To find the length of PQ, we use the sine rule in triangle POQ:

\(\frac{PQ}{2} = 10 \times \sin 1.1\)

\(PQ = 2 \times 10 \times \sin 1.1 = 17.8 \text{ cm}\)

(ii) First, find angle OPQ:

\(\angle OPQ = \frac{\pi}{2} - 1.1 \approx 0.471 \text{ radians}\)

Next, calculate the arc length QR:

\(\text{Arc } QR = 17.8 \times \left(\frac{\pi}{2} - 1.1\right) \approx 8.39 \text{ cm}\)

Finally, find the perimeter of the shaded region:

\(\text{Perimeter} = 17.8 + 10 + 10 + 8.39 = 26.2 \text{ cm}\)