Rhombus

Symmetries of square

Rhombus1

Isohedral tiling p4-55

Isohedral tiling p4-51c

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Rhombic star tiling

TrigonalTrapezohedron

Rhombus is a type of quadrilateral characterized by four sides of equal length and opposite sides that are parallel to each other. The angles opposite each other are equal, making the rhombus a special case of the parallelogram. A distinguishing feature of a rhombus is that all its sides have the same length, unlike other parallelograms such as the rectangle or the square, which have their own unique properties.

Properties

A rhombus has several distinctive properties:

• All four sides are of equal length.
• Opposite angles are equal.
• The diagonals of a rhombus bisect each other at right angles (90 degrees).
• The diagonals bisect the angles of the rhombus.
• The sum of the four interior angles is always 360 degrees, as is the case with any quadrilateral.

Diagonals

The diagonals of a rhombus have special properties:

• They bisect each other at right angles.
• Each diagonal divides the rhombus into two congruent triangles.
• The diagonals bisect the angles from which they are drawn.

Area and Perimeter

The area A of a rhombus can be calculated using the formula: \[A = \frac{d_1 \times d_2}{2}\] where \(d_1\) and \(d_2\) are the lengths of the diagonals.

The perimeter P of a rhombus is given by: \[P = 4 \times \text{side length}\]

Applications

Rhombuses are found in various applications ranging from architecture and design to the natural world. In geometry, the properties of rhombuses are used to solve problems related to space and shape. They are also seen in tiling patterns and in the design of certain kites that rely on the rhombus shape for stability in flight.

See Also

• Quadrilateral
• Parallelogram
• Rectangle
• Square
• Geometry