In the diagram, \(ABCD\) is a rectangle. Point \(E\) is outside the rectangle so that \(\triangle AED\) is an isosceles right-angled triangle with hypotenuse \(AD\). Point \(F\) is the midpoint of \(AD\), and \(EF\) is perpendicular to \(AD\).

If \(BC=4\) and \(AB=3\), determine the area of \(\triangle EBD\).