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

The area of triangle AOT is given by:

\(\frac{1}{2} \times AT \times r\)

Using trigonometry, \(\tan \theta = \frac{AT}{r}\), so \(AT = r \tan \theta\).

Thus, the area of triangle AOT is:

\(\frac{1}{2} r^2 \tan \theta\)

The area of sector AOB is:

\(\frac{1}{2} r^2 \theta\)

Therefore, the area of the shaded region is:

\(\frac{1}{2} r^2 \tan \theta - \frac{1}{2} r^2 \theta\)

(ii) For r = 3 and \theta = 1.2, we find the perimeter of the shaded region.

First, calculate AT:

\(\tan \theta = \frac{AT}{3} \Rightarrow AT = 3 \tan 1.2 \approx 7.716\)

The arc length of AB is:

\(r \theta = 3 \times 1.2 = 3.6\)

Using the Pythagorean theorem or trigonometry, find OT:

\(OT = \frac{3}{\cos 1.2} \approx 8.279\)

The perimeter of the shaded region is:

\(AT + \text{arc length} + OT - r = 7.716 + 3.6 + 8.279 - 3 = 16.6\)