The diagram shows the shaded region \(ABCD\). The lines \(AC\) and \(BD\) each have length \(12\text{ cm}\) and bisect each other at \(O\). The lines \(AD\) and \(BC\) are parallel and each has length \(4\text{ cm}\). The arcs \(AB\) and \(DC\) are part of a circle with centre \(O\).

(a) Find the obtuse angle \(AOB\), giving your answer in radians.

(b) Use your answer to part (a) to find

(i) the perimeter of the shaded region,

(ii) the area of the shaded region.