represents a parallelogram with origin p and directions v1 and v2.

Details and Options


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Basic Examples  (3)

A standard parallelogram:

Different styles applied to a parallelogram:

Compute the Area of a parallelogram:


Scope  (16)

Graphics  (6)

Specification  (2)

A standard parallelogram:

A parallelogram with specified origin and directions:

Styling  (2)

Color directives specify the face color:

FaceForm and EdgeForm can be used to specify the styles of the interior and boundary:

Coordinates  (2)

Use Scaled coordinates:

Use Offset coordinates:

Regions  (10)

Embedding dimension is the dimension of the space in which the vertices exist:

Geometric dimension is the dimensionality of the region itself:

Point membership test:

Get conditions for point membership:

Measure and centroid:

Distance from a point to a parallelogram:


Signed distance to a parallelogram:


Nearest point:


A parallelogram is bounded and convex:

Compute a bounding box:

Integrate over a parallelogram:

Optimize over a parallelogram:

Solve equations in a parallelogram:

Applications  (5)

A rhombus is a parallelogram in which all edges are the same length:


A parallelogram with sides that form right angles is a rectangle:


Any rectangle can easily be converted to a parallelogram:

The area of a parallelogram can easily be computed from the direction vectors:

Simply treat the vectors as a matrix and take the absolute value of the determinant:

Compare with Area:

A Parallelogram can tile the plane:

Properties & Relations  (6)

Rectangle is a special case of Parallelogram:

Polygon is a generalization of Parallelogram:

Parallelepiped generalizes Parallelogram to any dimension:

ImplicitRegion can represent any parallelogram:

ParametricRegion can represent any parallelogram:

A parallelogram can be represented as the union of two triangles:

Wolfram Research (2014), Parallelogram, Wolfram Language function, (updated 2019).


Wolfram Research (2014), Parallelogram, Wolfram Language function, (updated 2019).


Wolfram Language. 2014. "Parallelogram." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2019.


Wolfram Language. (2014). Parallelogram. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_parallelogram, author="Wolfram Research", title="{Parallelogram}", year="2019", howpublished="\url{}", note=[Accessed: 21-June-2024 ]}


@online{reference.wolfram_2024_parallelogram, organization={Wolfram Research}, title={Parallelogram}, year={2019}, url={}, note=[Accessed: 21-June-2024 ]}