The diagram shows a circle with centre \(O\) and radius \(10\) cm. The points \(A\), \(B\), \(C\) and \(D\) lie on the circle such that the chord \(AB=15\) cm and the chord \(CD=10\) cm. The chord \(AB\) is parallel to the chord \(DC\).

(i) Show that the angle \(AOB\) is \(1.70\) radians correct to 2 decimal places.

(ii) Find the perimeter of the shaded region.

(iii) Find the area of the shaded region.