# 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 xy-xy, 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,y

i

i

1

n

1

2

n

∑

i=1

i

i+1

i+1

i

x=x

n+1

1

y=y

n+1

1