Answer
No. You need to know the lengths of the diagonals.
Work Step by Step
No. You cannot calculate the area without knowing the lengths of the diagonals. There is one exception, and that is if it is a square because then you could calculate the lengths of the diagonals by using the Pythagorean Theorem.
The formula to find the area of a rhombus is: A=$\frac{1}{2}$$d_{1}$$d_{2}$