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TriangleMeasurement
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TriangleMeasurement

[Experimental]

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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

open allclose all

Basic Examples  (2)Summary of the most common use cases

Calculate the semiperimeter of a triangle:

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-u8pc65
Out[2]=2

Calculate the exradius of a triangle at the specified vertex:

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-k8g0w0
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-9bh167
Out[2]=2

Calculate all of the exradii:

In[3]:=3
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https://wolfram.com/xid/0dqu5z3hhoa-2u24g5
Out[3]=3

Scope  (11)Survey of the scope of standard use cases

Calculate the area of a triangle:

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-uiy0wr
Out[1]=1

Calculate the area using symbolic coordinates:

In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-suc30t
Out[2]=2

Calculate the circumradius of a triangle:

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-bwlr9q
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-77w7e
Out[2]=2

Calculate the exradius of a triangle at the specified vertex:

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-inagm6
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-qytb82
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-hm0i0g
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-oa47yd
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-mvigs8
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-grom1y
Out[2]=2

Calculate the height of a triangle:

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-wt6sea
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-zqs2np
Out[2]=2

Calculate the inradius of a triangle:

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-dyb72t
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-2cuo8o
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-vm2xpd
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-kfgk0
Out[2]=2

Calculate the nine-point center of a triangle:

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-7wvxu8
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-cnrtqy
Out[2]=2

Calculate the perimeter of a triangle:

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-n3dmpo
Out[1]=1

Calculate the semiperimeter of a triangle:

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-biw197
Out[1]=1

Properties & Relations  (11)Properties of the function, and connections to other functions

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

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-8v4r6a
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-m7qctv
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-7rw40i
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-0mjlkq
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-lh74d4
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-u3o219
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-ijtcwp
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-bahhu9
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-rfkpg9
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-xdr0ym
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-h1oil7
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-729w5r
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0dqu5z3hhoa-q9shvz
Out[3]=3

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

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-5icuh8
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-kuoj2p
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0dqu5z3hhoa-dmgrdy
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-t6ev1i
Out[2]=2

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

In[1]:=1
✖
https://wolfram.com/xid/0dqu5z3hhoa-c0dkwv
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqu5z3hhoa-oep5t6
Out[2]=2

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

In[1]:=1
✖
https://wolfram.com/xid/0dqu5z3hhoa-1pmoil
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0dqu5z3hhoa-wt2viv
Out[2]=2

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

In[1]:=1
✖
https://wolfram.com/xid/0dqu5z3hhoa-nm6n98
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0dqu5z3hhoa-kvarjs
Out[2]=2
Wolfram Research (2019), TriangleMeasurement, Wolfram Language function, https://reference.wolfram.com/language/ref/TriangleMeasurement.html.
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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.

✖
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.

✖
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

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

BibTeX

@misc{reference.wolfram_2025_trianglemeasurement, author="Wolfram Research", title="{TriangleMeasurement}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/TriangleMeasurement.html}", note=[Accessed: 29-March-2025 ]}

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@misc{reference.wolfram_2025_trianglemeasurement, author="Wolfram Research", title="{TriangleMeasurement}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/TriangleMeasurement.html}", note=[Accessed: 29-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_trianglemeasurement, organization={Wolfram Research}, title={TriangleMeasurement}, year={2019}, url={https://reference.wolfram.com/language/ref/TriangleMeasurement.html}, note=[Accessed: 29-March-2025 ]}

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@online{reference.wolfram_2025_trianglemeasurement, organization={Wolfram Research}, title={TriangleMeasurement}, year={2019}, url={https://reference.wolfram.com/language/ref/TriangleMeasurement.html}, note=[Accessed: 29-March-2025 ]}