In this question, all dimensions are in centimetres.

The diagram shows an isosceles triangle \(ABC\), where \(AB=AC\). The point \(M\) is the mid-point of \(BC\).

Given that \(AM=3+2\sqrt5\) and \(BC=4+6\sqrt5\), find, without using a calculator,

(i) the area of triangle \(ABC\),

(ii) \(\tan ABC\), giving your answer in the form \(\frac{a+b\sqrt5}{c}\), where \(a\), \(b\) and \(c\) are positive integers.