1. What is the minimum area of a lattice polygon that contains at least two interior lattice points?
1. According to the theorem for calculating the area of a lattice polygon, the area of the polygon $S \geqslant \frac{1}{2} \times 3+2-1=\frac{5}{2}$. On the other hand, taking points $A(0,0), B(1,4)$, and $C(2,3)$, then $\triangle A B C$ contains two lattice points, and the area of $\triangle A B C$ is equal to $\frac{5}{2}$. Therefore, the minimum value of the area sought is $\frac{5}{2}$.