Since the diagonal intersection angle is 90 degree in a rhombus, so using Pythagoras equation find out the other diagonal.
For example, if the rhombus is ABCD such that AB=BC=CD=DA='a' and AC='d1', then BD will be the other diagonal. Let say BD='d2'.
Now the area of the rhombus is given by (0.5 x d1 x d2). If 'a' and 'd1' is given, then we can write a^2 = (0.5xd1)^2 + (0.5xd2)^2, (Pythagoras equation) since the two diagonals are perpendicular to each other. So find 'd2' from this equation and insert into the equation of the area to calculate it.
For example, if the rhombus is ABCD such that AB=BC=CD=DA='a' and AC='d1', then BD will be the other diagonal. Let say BD='d2'.
Now the area of the rhombus is given by (0.5 x d1 x d2). If 'a' and 'd1' is given, then we can write a^2 = (0.5xd1)^2 + (0.5xd2)^2, (Pythagoras equation) since the two diagonals are perpendicular to each other. So find 'd2' from this equation and insert into the equation of the area to calculate it.