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Signed 2D Triangle Area from the Cross Product of Edge Vectors
The signed area of a triangle
in the

plane with vertices
,
,
is given by half the
component of the cross product
of the edge vectors
and
.
Contributed by:
Jim Arlow
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The edge vectors are
,
.
The cross product of the edge vectors is
.
The signed triangle area is half the
component of the cross product:
,
which is equivalent to half the determinant of the matrix formed by the coordinates of
when it is embedded in 3D space at
:
.
Reference
[1] J. O'Rourke,
Computational Geometry in C (Cambridge Tracts in Theoretical Computer Science)
, 2nd ed.
,
Cambridge: Cambridge University Press, 1998.
RELATED LINKS
Triangle Calculator
(
Wolfram Demonstrations Project
)
The Area of a Triangle Using a Determinant
(
Wolfram Demonstrations Project
)
Signed Area of a Polygon
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
Jim Arlow
"
Signed 2D Triangle Area from the Cross Product of Edge Vectors
"
http://demonstrations.wolfram.com/Signed2DTriangleAreaFromTheCrossProductOfEdgeVectors/
Wolfram Demonstrations Project
Published: April 28, 2014
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