In the diagram, AB is an arc of a circle with centre O and radius 4cm. Angle

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In the diagram, AB is an arc of a circle with centre O and radius 4cm.
Angle AOB is α radians. The point D on OB is such that AD is perpendicular to OB.
The arc DC, with centre O, meets OA at C.


i. Find an expression in terms of α for the perimeter of the shaded region ABDC.
ii. For the case where


find the area of the shaded region ABDC, giving your answer in the form kπ , where k is a constant to be determined.

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