Questions: Is this statement true or false? Pick's Theorem does not work for lattice polygons with holes.

Solution Steps

Pick's Theorem provides a method to calculate the area of a simple polygon whose vertices are lattice points (points with integer coordinates) on a grid. The theorem states: Area = I + B/2 - 1, where 'I' is the number of lattice points in the interior of the polygon, and 'B' is the number of lattice points on the boundary of the polygon.

Pick's Theorem, in its standard form, applies only to simple polygons, which are polygons without holes. A polygon with a hole inside it is no longer a simple polygon.

The statement "Pick's Theorem does not work for lattice polygons with holes" is true. Attempting to use the standard form of Pick's theorem directly on a polygon with holes will yield an incorrect result for the area. There are generalizations of Pick's theorem that can handle polygons with holes, but the basic form does not.

Final Answer