The area of the triangle with vertices [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex] is
[tex]\frac{1}{2}\left|\begin{array}{ccc}1&x_1&y_1\\1&x_2&y_2\\1&x_3&y_3\end{array}\right|[/tex].
Inserting numerical values, the are of the triangle with vertices (0, 0), (6, 2), (4, 8) is
[tex]\Delta = \frac{1}{2}\left|\begin{array}{ccc}1&0&0\\1&6&2\\1&4&8\end{array}\right |\\ \Delta = 0.5(48-8)\\ \Delta = 20 \;square\; units[/tex]
