Shoelace Formula

The shoelace formula, also known as Gauss's area formula and the surveyor's formula, is a mathematical algorithm for finding the area of a simple polygon whose vertices are given by their Cartesian coordinates in the plane. It takes its name from the constant cross multiplication of coordinates around the polygon, which resembles the lacing of a shoe. The formula was described by Albrecht Ludwig Friedrich Meister in 1769 and rests on the trapezoid formula described by Carl Friedrich Gauss and Carl Gustav Jacob Jacobi, and its triangle form can be seen as a special case of Green's theorem. It has practical applications in surveying and forestry, and can even be applied to self overlapping polygons, for which it shows that the computed area comes out the same regardless of how the overlapping shape is interpreted. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/