Do not use a calculator in this question.

The diagram shows the trapezium \(ABCD\) in which angle \(ADC\) is \(90^\circ\) and \(AB\) is parallel to \(DC\). It is given that

\(AB=4+3\sqrt5,\qquad DC=11+2\sqrt5,\qquad AD=7+\sqrt5.\)

(i) Find the perimeter of the trapezium, giving your answer in simplest surd form.

(ii) Find the area of the trapezium, giving your answer in simplest surd form.

The line \(y=2x+1\) intersects the curve \(xy=14-2y\) at the points \(P\) and \(Q\). The midpoint of \(PQ\) is \(M\).

(i) Show that the point \(\left(-10,\dfrac{23}{8}\right)\) lies on the perpendicular bisector of \(PQ\).

(ii) The line \(PQ\) intersects the \(y\)-axis at \(R\). The perpendicular bisector of \(PQ\) intersects the \(y\)-axis at \(S\). Find the area of triangle \(RSM\).