Angle ACD= Angle ADC= Angle BDO= Angle DBO, AD=AC.

So the triangle OBD is an isosceles triangle, that is, OB=OD.

So DO=5

In the isosceles triangle ABO, because AB=BO=5, AO=AD+DO=AC+OB=3+5=8, the two diagonals of the rhombus are perpendicular to each other.

BE=3, so the area of the triangle ABD =AD*BE/2=3*3/2=9/2.