Signed 2D Triangle Area from the Cross Product of Edge Vectors
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The signed area of a triangle 
in the 
-
plane with vertices 
, 
, 
is given by half the 
component of the cross product (InlineMath)z of the edge vectors 
and 
.
Contributed by: Jim Arlow (April 2014)
Open content licensed under CC BY-NC-SA
Snapshots
Details
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.
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