The diagram shows the curve \(y^2 = 2x - 1\) and the straight line \(3y = 2x - 1\). The curve and straight line intersect at \(x = \frac{1}{2}\) and \(x = a\), where \(a\) is a constant.

(i) Show that \(a = 5\).

(ii) Find, showing all necessary working, the area of the shaded region.