Rhombus

From Citizendium
Revision as of 01:00, 20 June 2009 by imported>Anthony Argyriou (fix a little)
Jump to navigation Jump to search
This article is a stub and thus not approved.
Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
This editable Main Article is under development and subject to a disclaimer.

A rhombus is a polygon of four sides of equal length. The angles of each pair of opposite vertices are equal. A rhombus is a special case of a parallelogram where all four sides are of equal length. A square is a special case of rhombus, where all four vertex angles are equal.

Properties

A rhombus with some mathematical properties shown

As with all quadrilaterals, the sum of the interior angles of a rhombus is 360 degrees; as with a parallelogram, it can be shown that the angles of opposite pairs of vertices are equal.

The perimeter of a rhombus is equal to 4 times the length of one side. The area of a square is equal to the length of the side multiplied by itself, multiplied by the sine of the angle between the sides.[1]

Any rhombus can tile a plane with no voids.

  1. Since the sum of the four angles is 360 degrees, and pairs of angles are equal, the sum of the angles of two adjacent vertices is 180 degrees. Since sin(180-x)=sin(x), the formula produces the same result no matter which vertex angle is chosen.