9459

Signed Area of a Polygon

The signed area of a polygon with vertices numbered through can be calculated exactly by the formula , where and . If the polygon is simple (non-intersecting sides), with the vertices numbered in a counterclockwise direction, the signed area is the area. This formula is surprisingly useful in surveying, architecture, and many other applications.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The formula for the area of a simple polygon can be elegantly derived using Green's theorem and extended to moments of the region.
S. F. Bockman, "Generalizing the Formula for Areas of Polygons to Moments," Amer. Math. Monthly, 96(2), 1989 pp. 131-132.
For more information, see:
S. Wagon, Mathematica in Action, 2nd ed., New York: Springer, 1999.

PERMANENT CITATION

    • 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 »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
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+