### PROBLEM LINK:

**Author:** Manish Pathak

**Tester:** Manish Pathak

**Editorialist:** Manish Pathak

### DIFFICULTY:

SIMPLE

### PREREQUISITES:

Maths

### PROBLEM:

A Polygon is drawn,whose vertices are points on a Lattice,a regularly spaced array of points.M and N are the number of inside and boundary points of the polygon respectively.You have to find the area of the polygon.

### EXPLANATION:

This can be solved by Pick’s Theorem.

According to Pick’s Theorem all you need to do to find the area of a polygon is to count the points on the interior and on the boundary of the shape.

Pick’s Theorem then states that:

Area= i+b/2-1

(i stands for the number of points in the interior of the shape, b stands for the number of points on the boundary of the shape.)

This link

might be helpful.

### AUTHOR’S AND EDITORIALIST’S SOLUTIONS:

Author’s and editorialist’s solution can be found here.