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\includegraphics[max width=\textwidth, alt={}, center]{3b527397-7781-41e9-8218-57277cc977bf-2_385_403_1866_872} The diagram shows a circle with centre \(O\). The circle is divided into two regions, \(R _ { 1 }\) and \(R _ { 2 }\), by the radii \(O A\) and \(O B\), where angle \(A O B = \theta\) radians. The perimeter of the region \(R _ { 1 }\) is equal to the length of the major \(\operatorname { arc } A B\).

1. Show that \(\theta = \pi - 1\).
2. Given that the area of region \(R _ { 1 }\) is \(30 \mathrm {~cm} ^ { 2 }\), find the area of region \(R _ { 2 }\), correct to 3 significant figures.