Overview
A rhombus is a four-sided polygon (quadrilateral) whose four sides have equal length. By definition every rhombus is a type of parallelogram, so opposite sides are parallel and opposite angles are equal. When all interior angles are right angles the rhombus becomes a square, but most rhombi have two acute and two obtuse angles.
Key properties
Several geometric features set rhombi apart. In a rhombus:
- Sides: all four sides are congruent.
- Opposite angles: equal in measure; adjacent angles are supplementary.
- Diagonals: they bisect each other, are perpendicular, and each diagonal bisects the interior angles at its endpoints.
- Symmetry: a rhombus typically has two lines of reflectional symmetry (unless it is a square, which has four).
Area and perimeter
The perimeter is simple: P = 4a, where a is the side length. There are several equivalent formulas for area. If d1 and d2 are the diagonal lengths, then area = (d1 * d2) / 2. Equivalently, if a is the side length and θ is any interior angle, area = a² sin(θ). The height (distance between a pair of parallel sides) can be used as base × height in the usual way.
History and terminology
The English name derives from the Greek word rhombos, meaning a spinning or whirling object such as a top. Informally, rhombi are often called diamonds, especially when presented as a rotated square in design and card suits; however, the term "diamond" is a stylistic label rather than a precise geometric classification.
Examples, uses, and distinctions
Rhombi appear in art, tiling patterns, crystal structures (the rhombohedral lattice), and architecture. In classification, every square is a rhombus but not every rhombus is a square. A rhombus is also a special kind of kite because it has two pairs of adjacent equal sides. These relationships help place the rhombus within the broader family of quadrilaterals used across mathematics and applied design.