# Signed Area of a Polygon

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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.

Contributed by: Bruce Atwood (Beloit College) and Stan Wagon (Macalester College) (March 2011)

After work by: Stan Wagon

Open content licensed under CC BY-NC-SA

## Snapshots

## 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

"Signed Area of a Polygon"

http://demonstrations.wolfram.com/SignedAreaOfAPolygon/

Wolfram Demonstrations Project

Published: March 7 2011