The diagram shows part of the curve \(y=2\sqrt{x}\). The normal to the curve at the point \(A(4,4)\) meets the \(x\)-axis at the point \(B\).

(i) Find the equation of the line \(AB\).

(ii) Find the coordinates of \(B\).

(iii) Showing all your working, find the area of the shaded region.