jmc

The area of $△ABC$ is equal to half the product of its base and height. By the Pythagorean Theorem, we find its height is $\sqrt{1^2+2^2}=\sqrt{5}$, and its base is $\sqrt{2^2+4^2}=\sqrt{20}$. We multiply these and divide by $2$ to find the area of the triangle is $\frac{\sqrt{5\cdot 20}}{2}=\frac{\sqrt{100}}{2}=\frac{10}{2}=5$. Since the grid has an area of $30$, the fraction of the grid covered by the triangle is $\frac{5}{30}=\boxed{\frac{1}{6}}$.