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.
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x
i
y
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1
n
1
2
n
∑
i=1
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y
i+1
x
i+1
y
i
x
n+1
x
1
y
n+1
y
1