Rhombus - a quadrilateral with sides of equal length; equivalently, a quadrilateral with mutually perpendicular and intersecting halves.
Each rhombus is a parallelogram and is also a deltoid. A special case of a rhombus is a square, which is a rhombus with right angles and at the same time is a rhombus with diagonals of the same length.

It has the following properties:

1. The rhombus is a convex figure.
2. The sum of the measures of all interior angles is 2 Π (360 °), and the sum of the measures of two adjacent interior angles is Π, $$ \alpha + \beta = 180° $$ means: $$ \alpha = 180° - \beta $$ $$ \beta = 180° - \alpha $$
3. The diagonals intersect at right angles dividing the rhombus into four congruent right triangles.
4. The point of intersection of the rhombus diagonals divides each of them into two halves, marking the center of the inscribed circle being the center of symmetry of the rhombus.
5. The diagonals coincide with the bisectors of the angles and the symmetry axes of the rhombus.
6. Formula on the longer diagonal of the rhombus on the side and angle
$$ f=2a\cos {\tfrac {\alpha }{2}} $$
7. Formula on the longer diagonal of the diamond from the area and the diagonal
$$ f=\frac{2\cdot S }{d} $$
8. Formula for the shorter diagonal of the diamond on the side and angle
$$ d=2a\sin {\tfrac {\alpha }{2}} $$
9. Formula for the shorter diagonal of the diamond from the area and the diagonal
$$ d=\frac{2\cdot S }{f} $$
10. Formula for height of the rhombus from the side and the surface area
$$ h=\frac{S}{a} $$
11. Formula for height of the rhombus from the angle and area
$$ h=\sqrt{S\cdot \sin(\alpha)} $$
12. Wzór na Area from the side and height
$$ S=a\cdot h $$
13. Formula for area from side and angle
$$ S=a^{2}\cdot \sin \alpha =a^{2}\cdot \sin \beta $$
14. Formula for area from height and angle
$$ S=\frac {h^{2}}{\sin \alpha } $$
15. Formula for area from diagonals
$$ S=\frac {d\cdot f}{2} $$
16. Formula for area from the side and radius of the inscribed circle
$$ S=2a\cdot r $$
17. Formula for perimeter of a Rhombus
$$ L= 4\cdot a $$
18. Formula for radius of the circle inscribed in the rhombus from the side and angle
$$ r={\tfrac {1}{2}}a\sin \alpha $$
19. Formula for radius of the circle inscribed in the rhombus from diagonals
$$ r={\frac {d\cdot f}{2{\sqrt {d^{2}+f^{2}}}}} $$