Area of a Polygon
The (signed) area of a planar polygon with vertices , , …, that is not self-intersecting is[more]
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.[less]