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this is a lattice its a set of evenly spaced points on a repeating grid the lattice points here are represented as being at the intersections of the dotted lines this is a simple lattice polygon its a polygon such that each of its Corners lie on the lattice points and its called Simple because its lines dont overlap or cross and it doesnt contain any holes we indicate the number of lattice points on the boundary of the polygon as B and the number of interior lattice points those contain strictly within the boundary of the polygon as I given a simple lattice polygon and asked to find this area its easy to get lost in complicated trigonometry when actually theres a simple formula known as pix theorem which applies to any simple lattice polygon pix theorem described by geogpick in 1899 says that the area of a simple lattice polygon a is equal to the number of interior lattice points plus half the number of boundary lattice points minus one in this video well prove this theorem fi