Final answer:
The formula for the area of a polygon with integer vertices is known as Pick's theorem. It states that the area of a simple polygon with integer vertex coordinates.
Step-by-step explanation:
The formula for the area of a polygon with integer vertices is known as Pick's theorem. It states that the area of a simple polygon with integer vertex coordinates is given by:
Area = I + (B/2) - 1
where:
- I is the number of lattice points (integer points) inside the polygon
- B is the number of lattice points on the perimeter of the polygon
For example, the area of a triangle with vertices (0, 0), (3, 0), and (3, 4) is 6. There are 4 lattice points inside the triangle and 8 lattice points on the perimeter, so the formula gives us:
Area = 4 + (8/2) - 1 = 6