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\includegraphics[max width=\textwidth, alt={}, center]{567c3d72-c633-4ae0-8605-f63f93d718c4-06_517_768_262_685} The diagram shows a circle with centre \(O\) and radius \(r \mathrm {~cm}\). Points \(A\) and \(B\) lie on the circle and angle \(A O B = 2 \theta\) radians. The tangents to the circle at \(A\) and \(B\) meet at \(T\).

1. Express the perimeter of the shaded region in terms of \(r\) and \(\theta\).
2. In the case where \(r = 5\) and \(\theta = 1.2\), find the area of the shaded region.