The diagram shows a circle, centre \(O\), radius \(8\text{ cm}\). Points \(A,B,C,D\) lie on the circumference such that \(AB\) is parallel to \(DC\). The length of the arc \(AD\) is \(4\text{ cm}\), and the length of the chord \(AB\) is \(15\text{ cm}\).

(i) Find, in radians, \(\angle AOD\).

(ii) Hence show that \(\angle DOC=1.43\) radians, correct to 2 decimal places.

(iii) Find the perimeter of the shaded region.

(iv) Find the area of the shaded region.