Rhombus

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

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