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In geometry, a rhombus is a quadrilateral whose four sides are of equal length. It is a special case of the parallelogram; a rhombus with right angles is a square.

Rhombi hold the following properties:

  • All four sides are of equal length (congruent)
  • Opposite sides are parallel to one another
    • Parallelogram
  • Opposite angles are of equal measure (congruent)
  • Adjacent angles are supplementary to one another
  • Diagonals bisect the angles of the corners they connect
  • Diagonals bisect one another
  • Diagonals intersect at right angles

Diangle lengths

$ \begin{align}p&=a\sqrt{2\bigl(1-\cos(\theta)\bigr)}\\q&=a\sqrt{2\bigl(1+\cos(\theta)\bigr)}\end{align} $

Area

$ A=a^2\sqrt{1-\cos^2(\theta)} $

Circumcircle

$ R=\frac{a}{\sqrt{2\sin^2(\theta)}} $

Incircle

$ r=\frac{a\sin(\theta)}{2} $