4 The diagram shows the curve \(C\) with polar equation $$r = 6 ( 1 - \cos \theta ) , \quad 0 \leqslant \theta < 2 \pi$$ \includegraphics[max width=\textwidth, alt={}, center]{06ae13de-5cf3-421d-ac7a-ee9f74b653be-3_552_903_922_550}

1. Find the area of the region bounded by the curve \(C\).
2. The circle with cartesian equation \(x ^ { 2 } + y ^ { 2 } = 9\) intersects the curve \(C\) at the points \(A\) and \(B\).
   1. Find the polar coordinates of \(A\) and \(B\).
   2. Find, in surd form, the length of \(A B\).