Polygon Basics


You must have come across various figures with many sides. Polygons are many-sided figures formed by straight line segments. Polygons are a family of figures, which may be different from each other as one may have more sides than the other. However, they bear different names according to the number of sides they possess. There are different types of polygons and some of the most familiar ones are triangle, rectangle and the square. The polygons, which have equal sides, are called regular polygons.

Names of polygons with different number of sides

Each polygon figure has a particular number of sides, number of vertices, number of diagonals and number of angles. The following chart would provide a better knowledge about the different types of polygons.

Polygons # of Sides # of Vertices # of Diagonals # of Angles
Triangle 3 3 0 3
Quadrilateral 4 4 2 4
Pentagon 5 5 5 5
Hexagon 6 6 9 6
Heptagon 7 7 14 7
Octagon 8 8 20 8
Nonagon 9 9 27 9
Decagon 10 10 35 10



Though the word Polygon in Greek is a combination of “poly” meaning many and “gon” meaning angle, yet polygons also have important features in the form sides and vertices. You can also separate a polygon by drawing all the diagonals and it can be done by drawing from one single vertex. If you consider the above figure EFGH, which is a rectangle, you can separate the polygon by drawing the diagonal from vertex E to vertex G thus dividing the polygon into two triangles EFG and triangle EGH.



Triangle is the simplest form of polygon and it has three angles. Apart from that, it also has three sides and three vertices. The ‘three’ factor is very much associated with the word triangle as “tri” means three.

Regular polygons


Regular polygons are the ones, which have all their sides congruent and equal.

Finding out the summation of interior angles of a quadrilateral (having four sides):

There is a very easy way to find out the sum of the interior angles of a polygon. If you consider “n” as the number of sides or angles that a polygon has then, you can use the formula to calculate the sum of the interior angles of a square. As a square has 4 sides you need take 4 in place of “n”.

sum of angles = ( n – 2 )180°
sum of angles = ( 4 – 2 )180°
sum of angles = 2 x 180°
sum of angles = 360°

Finding out the summation of interior angles of a quadrilateral (having five sides):

Similarly, you can also calculate the summation of the interior angles of a pentagon with the help of the same formula ( n – 2 )180°, where n is the number of sides.

In case of a Pentagon:

Sum of angles = ( n – 2 )180°
Sum of angles = ( 5 – 2 )180°, as n = 5 in this case
Sum of angles = 3 x 180°
Sum of angles = 540°



Referring to the above 8-sided figure ABCDEFGH, we can say it is an Octagon. By drawing diagonals from the same vertex A to all the vertices, we can have 6 triangles. We can also find the summation of all the angles of this Regular Polygon, using the formula (n – 2)180°, where “n” is the total number of sides of the polygon.

Sum of the sides of the Octagon = (8-2) 180°
Sum of the sides of the Octagon = (6) 180°
Sum of the sides of the Octagon = 1080°

Test your knowledge – try our Polygon Basics Test.