Rhombus

A Quadrilateral with both pairs of opposite sides Parallel and all sides the same length, i.e., an equilateral Parallelogram. The word Rhomb is sometimes used instead of rhombus, and a rhombus is sometimes also called a diamond. The Diagonals $p$ and $q$ of a rhombus are perpendicular and satisfy

$$p^2+q^2=4a^2,$$

The Area of a rhombus is given by

$$A={\textstyle{1\over 2}}pq.$$

A rhombus whose Acute Angles are 45° is called a Lozenge.

See also Diamond, Lozenge, Parallelogram, Quadrilateral, Rhombic Dodecahedron, Rhombic Icosahedron, Rhombic Triacontahedron, Rhomboid, Skew Quadrilateral, Trapezium, Trapezoid

References

Beyer, W. H. (Ed.) CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 123, 1987.