(i) To find the perimeter of the shaded region, we first calculate the length of the major arc. The angle of the major arc is given by:

\(2\pi - 2.2 = 4.083\) radians.

The length of the major arc is:

\(s = r\theta = 6 \times 4.083 = 24.5\) cm.

The perimeter of the shaded region is the sum of the lengths of the two radii and the major arc:

\(6 + 6 + 24.5 = 36.5\) cm.

(ii) The area of the major sector is given by:

\(\frac{1}{2} r^2 \theta = \frac{1}{2} \times 6^2 \times 4.083 = 73.49\) cm².

The area of triangle AOB is given by:

\(\frac{1}{2} \times 6^2 \times \sin 2.2 = 14.55\) cm².

The ratio of the area of the shaded region to the area of triangle AOB is:

\(\frac{73.49}{14.55} = 5.05\).

Thus, the ratio is 5.05 : 1.