The diagram shows a company logo, \(ABCD\). The logo is part of a sector, \(AOB\), of a circle, centre \(O\) and radius \(50\) cm. The points \(C\) and \(D\) lie on \(OB\) and \(OA\) respectively. The lengths \(AD\) and \(BC\) are equal and \(AD:AO=7:10\). The angle \(AOB\) is \(\dfrac{4\pi}{9}\) radians.

(i) Find the perimeter of \(ABCD\).

(ii) Find the area of \(ABCD\).