11453
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
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
THINGS TO TRY
Rotate and Zoom in 3D
Slider Zoom
Gamepad Controls
Automatic Animation
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.
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
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Construction for Three Vectors with Sum Zero
Izidor Hafner
Triangle Interior
Ed Pegg Jr
The Triangle Inequality
Chris Boucher
Signed Area of a Polygon
Bruce Atwood (Beloit College) and Stan Wagon (Macalester College)
Area of a Triangle
Norm Prokup
The Area of a Triangle as Half a Rectangle
Jay Warendorff
A Relation between the Areas of Four Triangles
Jay Warendorff
The Area of the Contact Triangle
Jay Warendorff
Rational Triangles with Area Less than 102
Jaime RangelMondragon
The Area of a Triangle inside the Incircle
Jay Warendorff
Related Topics
3D Graphics
Area
Triangles
Vector Algebra
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+