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The diagram shows a sector \(A O B\) of a circle with centre \(O\) and radius 5 cm . Angle \(A O B\) is \(\theta\) radians. The area of triangle \(A O B\) is \(8 \mathrm {~cm} ^ { 2 }\).
- Given that the angle \(\theta\) is obtuse, find \(\theta\).
The shaded segment in the diagram is bounded by the chord \(A B\) and the arc \(A B\).
- Find the area of the segment, giving your answer correct to 3 significant figures.
- Find the perimeter of the segment, giving your answer correct to 3 significant figures.