Rhombus: Difference between revisions
imported>Peter Schmitt m (→Properties: remove spurious </ref>) |
imported>Paul Wormer (I read the text as if a parallelogram had 4 equal sides, changed it) |
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{{Image|Rhombus.png|right|250px|A ''rhombus''. All sides (marked blue) are of equal length; opposite angles (same color arc) are equal; diagonals cross at right angles.}} | {{Image|Rhombus.png|right|250px|A ''rhombus''. All sides (marked blue) are of equal length; opposite angles (same color arc) are equal; diagonals cross at right angles.}} | ||
A '''rhombus''' or '''rhomb''' is a [[polygon]] | A '''rhombus''' or '''rhomb''' is a four-sided [[polygon]] (a [[quadrilateral]]) with sides of equal length. The angles of each pair of opposite vertices are equal. A rhombus is a special case of a [[parallelogram]], a quadrilateral with equal and parallel opposite sides. A [[square]] is a special case of a rhombus, where all four vertex angles are equal to 90°. | ||
==Properties== | ==Properties== | ||
As with all quadrilaterals, the sum of the interior angles of a rhombus is 360 degrees; as with a parallelogram, | As with all quadrilaterals, the sum of the interior angles of a rhombus is 360 degrees; | ||
as with a parallelogram, the angles of opposite pairs of vertices are equal, | |||
and the sum of the angles of two adjacent vertices is 180 degrees. | |||
The perimeter of a rhombus is equal to 4 times the length of one side. The area of a | The perimeter of a rhombus is equal to 4 times the length of one side. | ||
The area of a rhombus is equal to the length of the side multiplied by itself, | |||
multiplied by the [[sine]] of the angle between the sides. | |||
(Since sin(180-x)=sin(x) this does not depend on the choice of the angle.) | |||
Any rhombus can [[tile (mathematics)|tile]] a plane with no voids. | Any rhombus can [[tile (mathematics)|tile]] a plane with no voids. | ||
Revision as of 02:12, 20 November 2009
A rhombus or rhomb is a four-sided polygon (a quadrilateral) with sides of equal length. The angles of each pair of opposite vertices are equal. A rhombus is a special case of a parallelogram, a quadrilateral with equal and parallel opposite sides. A square is a special case of a rhombus, where all four vertex angles are equal to 90°.
Properties
As with all quadrilaterals, the sum of the interior angles of a rhombus is 360 degrees; as with a parallelogram, the angles of opposite pairs of vertices are equal, and the sum of the angles of two adjacent vertices is 180 degrees.
The perimeter of a rhombus is equal to 4 times the length of one side. The area of a rhombus is equal to the length of the side multiplied by itself, multiplied by the sine of the angle between the sides. (Since sin(180-x)=sin(x) this does not depend on the choice of the angle.)
Any rhombus can tile a plane with no voids.