# TriangleMeasurement

TriangleMeasurement[tri,type]

gives the specified type of measurement for the triangle tri.

# Details

• The triangle tri can be given as {p1,p2,p3}, Triangle[{p1,p2,p3}] or Polygon[{p1,p2,p3}].
• The following measurement types can be given:
•  "Area" area "Circumradius" radius of circumcircle {"Exradius",p} radius of excircle opposite vertex p {"ExteriorAngle",p} exterior angle at vertex p {"FullExteriorAngle",p} full exterior angle at vertex p {"Height",p} height of the triangle measured from vertex p "Inradius" radius of incircle {"InteriorAngle",p} interior angle at vertex p "NinePointRadius" radius of nine-point circle "Perimeter" perimeter "Semiperimeter" semiperimeter
• In the form {"type",p}, p can be a symbolic point specification in a GeometricScene, or it can be an explicit vertex of the form {x,y}, Point[{x,y}] or the index i of the vertex. When given in the short form "type", the vertex p2 is used.
• In any form that specifies a vertex p, a value of All will return a list of three values corresponding to the vertices.
• TriangleMeasurement can be used with symbolic points in GeometricScene.

# Examples

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## Basic Examples(2)

Calculate the semiperimeter of a triangle:

Calculate the exradius of a triangle at the specified vertex:

Calculate all of the exradii:

## Scope(11)

Calculate the area of a triangle:

Calculate the area using symbolic coordinates:

Calculate the circumradius of a triangle:

Calculate the exradius of a triangle at the specified vertex:

Calculate the exterior angle of a triangle at the specified vertex:

Calculate the full exterior angle of a triangle at the specified vertex:

Calculate the height of a triangle:

Calculate the inradius of a triangle:

Calculate the interior angle of a triangle at the specified vertex:

Calculate the nine-point center of a triangle:

Calculate the perimeter of a triangle:

Calculate the semiperimeter of a triangle:

## Properties & Relations(11)

TriangleMeasurement[{a,b,c},"Area"] is equivalent to Area[Triangle[{a,b,c}]]:

TriangleConstruct[{a,b,c},"Circumcircle"] is equivalent to Circle[TriangleCenter[{a,b,c},"Circumcenter"],TriangleMeasurement[{a,b,c},"Circumradius"]]:

TriangleConstruct[{a,b,c},"Excircle"] is equivalent to Circle[TriangleCenter[{a,b,c},"Excenter"],TriangleMeasurement[{a,b,c},"Exradius"]]:

TriangleConstruct[{a,b,c},"ExteriorAngle"] is equivalent to PlanarAngle[{a,b,c},"Exterior"]:

TriangleConstruct[{a,b,c},"FullExteriorAngle"] is equivalent to PlanarAngle[{a,b,c},"FullExterior"]:

TriangleMeasurement[{a,b,c},"Height"] is equivalent to ArcLength[TriangleConstruct[{a,b,c},"Altitude"]]:

TriangleConstruct[{a,b,c},"Incircle"] is equivalent to Circle[TriangleCenter[{a,b,c},"Incenter"],TriangleMeasurement[{a,b,c},"Inradius"]]:

TriangleConstruct[{a,b,c},"InteriorAngle"] is equivalent to PlanarAngle[{a,b,c},"Interior"]:

TriangleConstruct[{a,b,c},"NinePointCircle"] is equivalent to Circle[TriangleCenter[{a,b,c},"NinePointCenter"],TriangleMeasurement[{a,b,c},"NinePointRadius"]]:

TriangleConstruct[{a,b,c},"Perimeter"] is equivalent to Perimeter[Triangle[{a,b,c}]]:

TriangleConstruct[{a,b,c},"Semiperimeter"] is equivalent to Perimeter[Triangle[{a,b,c}]]/2:

Wolfram Research (2019), TriangleMeasurement, Wolfram Language function, https://reference.wolfram.com/language/ref/TriangleMeasurement.html.

#### Text

Wolfram Research (2019), TriangleMeasurement, Wolfram Language function, https://reference.wolfram.com/language/ref/TriangleMeasurement.html.

#### CMS

Wolfram Language. 2019. "TriangleMeasurement." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TriangleMeasurement.html.

#### APA

Wolfram Language. (2019). TriangleMeasurement. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TriangleMeasurement.html

#### BibTeX

@misc{reference.wolfram_2023_trianglemeasurement, author="Wolfram Research", title="{TriangleMeasurement}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/TriangleMeasurement.html}", note=[Accessed: 22-September-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2023_trianglemeasurement, organization={Wolfram Research}, title={TriangleMeasurement}, year={2019}, url={https://reference.wolfram.com/language/ref/TriangleMeasurement.html}, note=[Accessed: 22-September-2023 ]}