Area of a lattice polygon with Pick's theorem

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Pick’s theorem gives the area of a polygon whose vertices lie on a unit lattice: $A = I + \dfrac{B}{2} - 1$, where $I$ is the number of lattice points inside the polygon and $B$ those on the boundary. A polygon has $12$ interior points and $14$ boundary points. What is its area?

Solution

Apply the formula directly: $A = I + \frac{B}{2} - 1 = 12 + \frac{14}{2} - 1 = 12 + 7 - 1 = \boxed{18}.$