# Signed Area of a Polygon

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.

{,}

x

i

y

i

1

n

1

2

n

∑

i=1

x

i

y

i+1

x

i+1

y

i

x

n+1

x

1

y

n+1

y

1