The diagram shows an isosceles triangle \(ABC\), where \(AB=AC=5\) cm. The arc \(BEC\) is part of the circle centre \(A\) and has length \(6.2\) cm. The point \(D\) is the midpoint of the line \(BC\). The arc \(BFC\) is a semi-circle centre \(D\).

(i) Show that angle \(BAC\) is \(1.24\) radians.

(ii) Find the perimeter of the shaded region.

(iii) Find the area of the shaded region.