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Rhombus plural: rhombi
Try this Drag the orange dots on each vertex
to reshape the rhombus. Notice how the four sides remain the same length and the opposite sides remain parallel.
(If there is no image below, see support page.)
A rhombus is actually just a special type of parallelogram.
Recall that in a parallelogram each pair of opposite sides are equal in length.
With a rhombus, all four sides are the same length.It therefore has all the properties of a parallelogram.
See Definition of a parallelogram
Its a bit like a square that can 'lean over'
and the interior angles need not be 90°.
Sometimes called a 'diamond' or 'lozenge' shape.
Properties of a rhombus
| Base |
Any side can be considered a base. Choose any one you like. If used to calculate the area (see below) the corresponding altitude must be used.
In the figure above one of the four possible bases has been chosen. |
| Altitude |
The altitude of a rhombus is the perpendicular distance
from the base to the opposite side (which may have to be extended). In the figure above, the altitude corresponding to the base CD is shown. |
| Area |
There are several ways to find the area of a rhombus. The most common is (base × altitude).
Each is described in Area of a rhombus |
| Perimeter |
Distance around the rhombus. The sum of its side lengths.
See Perimeter of a rhombus |
The Diagonals of a Rhombus
The diagonals of a rhombus always bisect each other at 90°.
Some find this surprising and not at all obvious.
Reshape the rhombus above and convince yourself that the diagonals always cross at right angles.
Related polygon topics
General
Types of polygon
Area of various polygon types
Perimeter of various polygon types
Angles associated with polygons
Named polygons
(C) 2007 Copyright John Page
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