(i) To find the radius \(OE\) of the arc \(CED\), we use the cosine rule in the triangle \(OEC\):

\(\cos(0.9) = \frac{OE}{6}\)

Solving for \(OE\), we get:

\(OE = 6 \cos(0.9) = 3.73 \text{ cm}\)

(ii) To find the area of the shaded region, we calculate the area of the large sector and subtract the area of the small sector:

The angle of the large sector is \(2\pi - 1.8\).

Area of the large sector:

\(\frac{1}{2} \times 6^2 \times (2\pi - 1.8) = 80.7 \text{ cm}^2\)

Area of the small sector:

\(\frac{1}{2} \times 3.73^2 \times 1.8 = 12.52 \text{ cm}^2\)

Total area of the shaded region:

\(80.7 + 12.52 = 93.2 \text{ cm}^2\)