Find the area of the triangle with vertices $(1, 1)$, $(4, 2)$ and $(2, 5)$.

Area $= \dfrac{1}{2}\left|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)\right| = \dfrac{1}{2}\left|1(2 - 5) + 4(5 - 1) + 2(1 - 2)\right| = \dfrac{1}{2}\left|-3 + 16 - 2\right| = \dfrac{11}{2}$. Forgetting the factor of one half gives 11.