The points A(1, 1), B(4, 2) and C(3, 5) are the corners of a triangle…

Step 1. The slopes. $AB$ has slope $\dfrac{2 - 1}{4 - 1} = \dfrac{1}{3}$. $BC$ has slope $\dfrac{5 - 2}{3 - 4} = -3$.

Step 2. The product. $\dfrac{1}{3} \times (-3) = -1$, so $AB$ is perpendicular to $BC$.

Step 3. The legs. $AB = \sqrt{3^2 + 1^2} = \sqrt{10}$ and $BC = \sqrt{1^2 + 3^2} = \sqrt{10}$.

Step 4. The area. $\dfrac{1}{2} \times \sqrt{10} \times \sqrt{10} = 5$.