No.
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You don't. There is not enough information. Different rhombuses with the same side lengths can have different areas, depending on the angles.
Equilateral? * * * * * No. Equilateral means only that the sides have equal lengths - not that the angles are also equal. A rhombus, for example is equilateral but not equiangular. The correct answer is "regular".
All sides of a rhombus are the same length. Of the other parallelograms, only the square has identical side lengths (it differs from a rhombus by having four right angles).
By using trigonometry
A rhombus has 4 right angles just like the square * * * * * In general a rhombus has a pair of equal obtuse angles and a pair of equal acute angles. It is only in a special case that the shape has 4 right angles and then it is called a square.