Area of a Triangle Using Determinants

The formula

For a triangle with vertices $(x_1,y_1)$, $(x_2,y_2)$, and $(x_3,y_3)$, the area is half the absolute value of this determinant:

The absolute value matters because the determinant itself can come out negative depending on the order the vertices are listed in. Area is never negative.

Worked example

Find the area of the triangle with vertices $(2,7)$, $(1,1)$, and $(10,8)$.

Solution: Expanding along the first row:

So the area is: