Question

Use calculus to find the area a of the triangle with the given vertices. (0, 0), (6, 2), (4, 8)

Answer 1

The area of the triangle with vertices  $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ is

$\frac{1}{2}\left|\begin{array}{ccc}1&x_1&y_1\\1&x_2&y_2\\1&x_3&y_3\end{array}\right|$.

Inserting numerical values, the are of the triangle with vertices (0, 0), (6, 2), (4, 8) is

$\Delta = \frac{1}{2}\left|\begin{array}{ccc}1&0&0\\1&6&2\\1&4&8\end{array}\right |\\ \Delta = 0.5(48-8)\\ \Delta = 20 \;square\; units$