The corners \( (x_1,y_1) \) and \( (x_2,y_2) \) and \( (x_3, y_3) \) of a triangle.
If \( (x_3,y_3)=(0,0) \)
The area of the triangle \( = \frac{1}{2} \begin{vmatrix} x_1 & y_1 \\ x_2 & y_2 \end{vmatrix} \)
otherwise, area \( = \frac{1}{2} \begin{vmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \\ \end{vmatrix} \)
the area of the parallelogram:

\( \begin{vmatrix} x_1 & y_1 \\ x_2 & y_2 \end{vmatrix} \)