6
\includegraphics[max width=\textwidth, alt={}, center]{02da6b6a-6db1-4bc3-ad4e-537e4f61dcac-3_412_629_258_758} The diagram shows a metal plate made by fixing together two pieces, \(O A B C D\) (shaded) and \(O A E D\) (unshaded). The piece \(O A B C D\) is a minor sector of a circle with centre \(O\) and radius \(2 r\). The piece \(O A E D\) is a major sector of a circle with centre \(O\) and radius \(r\). Angle \(A O D\) is \(\alpha\) radians. Simplifying your answers where possible, find, in terms of \(\alpha , \pi\) and \(r\),

1. the perimeter of the metal plate,
2. the area of the metal plate. It is now given that the shaded and unshaded pieces are equal in area.
3. Find \(\alpha\) in terms of \(\pi\).