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We prove area bounds for planar convex bodies in terms of their number ofinterior integral points and their lattice width data. As an application, weobtain sharp area bounds for rational polygons with a fixed number of interiorintegral points depending on their denominator. For lattice polygons, we alsopresent an equation for the area based on Noether's formula.

Area bounds for planar convex bodies containing a fixed number of interior integral points