Pick Formula for finding the area of Polygons
Pick Formula
Pick Formila
Drag the vertices of the polygons and count inner points and boundary points to find the area using Pick Formula (A) = I + B/2 -1.
Important Definitions:
Lattice Points: Lattice points are points in a coordinate system whose coordinates are all integers. In a two-dimensional Cartesian coordinate system, a lattice point is represented as ((x, y)), where both (x) and (y) are integers. For example, (1, 0), (-2, 4), etc., are lattice points, but (1/2 , 2), (1.5, 0) etc., are not lattice Points.
Lattice Polygon: A lattice polygon is a polygon whose vertices are lattice points, i.e., points with integer coordinates ((x, y)) in the Cartesian plane. These polygons are also called grid polygons or integral polygons.
For example:
- Square with vertices at ((0, 0), (2, 0), (2, 2), (0, 2)).
- Triangle with vertices at ((1, 1), (3, 1), (2, 4)).
- Hexagon with vertices at ((0, 0), (1, 1), (2, 0), (1, -1), (0, -1), (-1, 0)).