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In geometry, a rhombus (from Ancient Greek ῥόμβος - rrhombos, “rhombus, spinning top”), (plural rhombi or rhombuses) or rhomb (plural rhombs) is an equilateral quadrilateral. In other words, it is a four-sided polygon in which every side has the same length.

The rhombus is often casually called a diamond, after the diamonds suit in playing cards, or a lozenge, because those shapes are rhombi (though not all rhombi are actually diamonds or lozenges).

$Area=(\{D\_1\; times\; D\_2\})\; /2$

Because the rhombus is a parallelogram, the area also equals the length of a side (B) multiplied by the perpendicular distance between two opposite sides(H)

$Area=B\; times\; H$

The area also equals the square of the side multiplied by the sine of any of the exterior angles:

$Area=a^2\; sintheta$

where a is the length of the side and $theta$ is the angle between two sides.

If A, B, C and D were the vertices of the rhombus, named in agreement with the figure (higher on this page). Using $overrightarrow\{AB\}$ to represent the vector from A to B, one notices that

$overrightarrow\{AC\}\; =\; overrightarrow\{AB\}\; +\; overrightarrow\{BC\}$

$overrightarrow\{BD\}\; =\; overrightarrow\{BC\}+\; overrightarrow\{CD\}=\; overrightarrow\{BC\}-\; overrightarrow\{AB\}$.

The last equality comes from the parallelism of CD and AB.
Taking the inner product,

- $$

- $=\{ab\},\; overrightarrow\{bc\}>\; -\{ab\},\; overrightarrow\{ab\}>\; +\{bc\},\; overrightarrow\{bc\}>\; -\{bc\},\; overrightarrow\{ab\}>$

- $=\; 0$

Rhombic tiling |

This is also a called Tessellation.

- Parallelogram and Rhombus - Animated course (Construction, Circumference, Area)
- Rhombus definition. Math Open Reference With interactive applet.
- Rhombus area. Math Open Reference Shows three different ways to compute the area of a rhombus, with interactive applet.

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Last updated on Wednesday October 08, 2008 at 00:27:08 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Wednesday October 08, 2008 at 00:27:08 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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