(a) To find the perimeter of the shaded region, we first need to find the length of AC. Using the cosine rule:

\(AC^2 = 6^2 + 6^2 - 2 \times 6 \times 6 \times \cos(1.8)\)

\(AC = 9.40 \text{ cm}\)

Next, calculate the angle CAB:

\(\text{Angle } CAB = \frac{1}{2}(\pi - 1.8)\)

\(\text{Angle } CAB = 0.6708 \text{ radians}\)

Now, find the length of arc CD:

\(\text{Arc } CD = 9.40 \times 0.6708 = 6.306 \text{ cm}\)

The perimeter of the shaded region is:

\(6 + 3.40 + 6.306 = 15.7 \text{ cm}\)

(b) To find the area of the shaded region, calculate the area of sector ADC and subtract the area of triangle ABC:

\(\text{Area of sector } ADC = \frac{1}{2} \times 9.40^2 \times 0.6708\)

\(\text{Area of triangle } ABC = \frac{1}{2} \times 6^2 \times \sin(1.8)\)

\(\text{Area of shaded region} = 29.64 - 17.53 = 12.1 \text{ cm}^2\)