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\includegraphics[max width=\textwidth, alt={}, center]{5c1ab2aa-3609-4245-b87a-98ecedc83a11-2_606_579_895_785} The diagram shows a metal plate \(O A B C D E F\) consisting of 3 sectors, each with centre \(O\). The radius of sector \(C O D\) is \(2 r\) and angle \(C O D\) is \(\theta\) radians. The radius of each of the sectors \(B O A\) and \(F O E\) is \(r\), and \(A O E D\) and \(C B O F\) are straight lines.

1. Show that the area of the metal plate is \(r ^ { 2 } ( \pi + \theta )\).
2. Show that the perimeter of the metal plate is independent of \(\theta\).