 Shoelace formula

For a simple polygon with cyclically ordered vertices of a polygon $(x_i,y_i)$, its signed area is $\frac{1}{2}{\sum }_i(x_i{y}_{i+1}-x_{i+1}{y}_i)$, with indices read cyclically. Reversing the traversal changes the sign; taking the absolute value gives the area. Each summand is a two-dimensional determinant.