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.
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:
(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.)
might be helpful.
AUTHOR’S AND EDITORIALIST’S SOLUTIONS:
Author’s and editorialist’s solution can be found here.