Rhombus Area
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Area equals half the product of the two diagonals: A = (d₁ × d₂)/2. This works because a rhombus's diagonals always bisect each other at right angles, dividing the shape into four congruent right triangles.

This follows from the rhombus's defining property that all four sides are equal length, which forces the diagonals to be perpendicular bisectors of each other by symmetry. This perpendicularity is precisely what makes the simple diagonal-product formula valid; it wouldn't work for a general (non-rhombus) parallelogram.

Yes, a square is a special case of a rhombus, with all four angles equal to 90° in addition to equal sides, so the diagonal formula A = (d₁ × d₂)/2 applies directly. Since a square's two diagonals are also equal in length, this simplifies further to A = d²/2 for a square specifically.

The (d₁×d₂)/2 formula relies on the diagonals bisecting each other at a right angle, which is unique to rhombi (and squares) among parallelograms; a general parallelogram's diagonals cross at an angle other than 90° and don't necessarily bisect at that same point in the same simple way. Interestingly, kites do share the perpendicular-diagonal property, which is why a similar formula works for them too.

In that case, use the parallelogram side-angle formula instead, A = a² × sin(θ), since a rhombus is a parallelogram with all sides equal to a. Both formulas give the same correct area; which one to use just depends on which measurements you have available.