The diagram shows a circle, centre \(O\), radius \(12\text{ cm}\). The points \(A\) and \(B\) lie on the circumference of the circle and form a rectangle with points \(C\) and \(D\). The length of \(AD\) is \(8\text{ cm}\), and the area of the minor sector \(AOB\) is \(150\text{ cm}^2\).

(i) Show that angle \(AOB\) is \(2.08\) radians, correct to 2 decimal places.

(ii) Find the area of the shaded region \(ADCB\).

(iii) Find the perimeter of the shaded region \(ADCB\).