GRE Geometry | Polygons

The word polygon is derived from the Greek word polugonon, here poly means many and gons means angles. Polygons can be defined as a closed curve made up of line segments. Each line segment will become sides of the polygon.

Classification of polygons:
On the basis of the number of sides polygons are classified as follows:

For n sides, we can call it n-gon. From here we can observe that the triangle is a polygon with least number of sides.

Concave and Convex polygon:
Convex polygons are the polygons whose all diagonal lie inside the figure and Concave polygons are those whose any diagonal lie outside the figure.

Regular and Irregular polygon:
Regular polygons are the polygons having all sides of equal length and Irregular polygons are the polygons having different side length.


  • For a polygon, Exterior angle + Interior angle = 360°
  • The sum of all exterior angles of polygon is 360°
  • In a regular polygon all interior angles are equal.
  • In a regular polygon all exterior angles are also equal.
  • For a regular polygon, Number of sides = 360/exterior angle.
  • Sum of all interior angles of a polygon is given by (n-2)*180, where ‘n’ is the number of sides in the polygon.
  • Area of a polygon means area enclosed by the polygon and Perimeter of a polygon is sum of all the side length.