The formula is: s = (1/2) * (x1y2 *1+x2y3 *1+x3y1-x1y3 *1.

Let a (x 1, y 1), b (x2, y2), c (x3, y3)?

By a-> b-> c->； Turn counterclockwise. (determinant writing requirements) Let the area of a triangle be S, then S=( 1/2)* (determinant is as follows)?

|x 1 y 1 1|？

|x2 y2 1|？

|x3 y3 1|？

s =( 1/2)*(x 1 y2 * 1+x2y 3 * 1+x3y 1-x 1y 3 * 1-x2y 1 * 1)？

That is, the formula for calculating the triangle area with the coordinates of three vertices is: s = (1/2) * (x1y2+x2y3+x3y1-x1y3-x2y1-x3y2).

Mathematically, determinant is a function of matrix A whose domain is det, and its value is scalar, and it is denoted as det(A) or | A |. Whether in linear algebra, polynomial theory or calculus (such as substitution integral method), determinant, as a basic mathematical tool, has important applications.

Determinant can be regarded as a generalization of the concept of directed area or volume in general Euclidean space. In other words, in N-dimensional Euclidean space, determinant describes the influence of a linear transformation on "volume".