Area of a Polygon

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The (signed) area of a planar polygon with vertices , , …, that is not self-intersecting is

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or in terms of 2×2 determinants,

.

To calculate the formula, form a three-column matrix of rows , , , ... , .

To this matrix append the column +, , , ..., , and the column , , , ..., , .

The area is the arithmetic mean of the sum of the terms in the "+" column and the sum of of the terms in the "" column.

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Contributed by: Izidor Hafner (June 2018)
Open content licensed under CC BY-NC-SA


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