8 The diagram shows a sketch of the curve \(C\) with polar equation
$$r = 3 + 2 \cos \theta , \quad 0 \leqslant \theta \leqslant 2 \pi$$
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- Find the area of the region bounded by the curve \(C\).
- A circle, whose cartesian equation is \(( x - 4 ) ^ { 2 } + y ^ { 2 } = 16\), intersects the curve \(C\) at the points \(A\) and \(B\).
- Find, in surd form, the length of \(A B\).
- Find the perimeter of the segment \(A O B\) of the circle, where \(O\) is the pole.