Enter the number of interior points and boundary points into the calculator to determine the area of a simple polygon using Pick’s Theorem. Pick’s Theorem relates the area of a simple polygon with lattice points to the number of interior and boundary points.
Pick’s Theorem Formula
The following formula is used to calculate the area of a simple polygon based on Pick’s Theorem.
A = i + frac{b}{2} - 1Variables:
- A is the area of the simple polygon (units2)
- i is the number of interior points
- b is the number of boundary points
To calculate the area of a simple polygon using Pick’s Theorem, add the number of interior points to half the number of boundary points and subtract one.
What is Pick’s Theorem?
Pick’s Theorem provides a formula to calculate the area of simple polygons whose vertices are points on a lattice. A lattice point is a point with integer coordinates. According to the theorem, the area of such a polygon can be determined by the number of lattice points located in the interior of the polygon and the number of lattice points on the boundary. This theorem is particularly useful in the field of discrete geometry.
How to Calculate Area using Pick’s Theorem?
The following steps outline how to calculate the area of a simple polygon using Pick’s Theorem.
- First, count the number of interior points (i) within the simple polygon.
- Next, count the number of boundary points (b) on the edges of the polygon.
- Use the formula from above: A = i + b/2 – 1.
- Finally, calculate the area (A) of the simple polygon in square units.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Number of interior points (i) = 7
Number of boundary points (b) = 12
