Learn All About Polygons And Their Types Based On Sides

Polygon term originates from the two Greek words "Poly" and "Gon", where "Poly" stands for "many" and "Gon" stands for angle. So the complete word "Polygon" deals with shapes having many angles.

Curves are used to draw a polygon. A polygon is a shape with many sides or angles. It also has edges, vertices and diagonals. Interestingly, the number of angles in a shape is always equal to the number of edges or sides in a polygon. We can visualise and count the angles, edges, vertices and diagonals in a polygon.

Curve

Curve is a plane figure formed by joining a number of points without lifting a pencil from paper and without retracing any portion of drawing.

A curve which does not intersect itself at any point is called an open curve and on the other hand, a curve which intersects itself is called a closed curve.

Examples of curves

Polygon

Polygon is a closed curve which is made up of only finite number of line segments and any two line segments do not intersect each other except at their end points. It is a two dimensional figure in geometry.

The line segments of a polygon are called sides or edges and end points of the line segments are called its vertices or corners.

Examples of polygons

Adjacent sides

Any two sides of a polygon with a common end point are called adjacent sides of the polygon.

Adjacent vertices

The end points of a side of a polygon are called adjacent vertices.

Diagonals

A diagonal is a line segment which is formed by joining two vertices which are not adjacent.

Example of diagonal

AC and BD are diagonals.

Types of polygon

Convex polygon

A polygon is said to be a convex polygon, if its diagonals completely lie inside of it. Its interior angles are less than 180 degrees.

Examples of convex polygon

Concave polygon

A polygon is said to be a concave polygon, if its diagonals completely lie outside of it. Its one or more than one interior angle is more than 180 degrees.

Examples of concave polygon

Regular polygon

A regular polygon is a polygon whose all sides and all angles are equal. In other words we can say, it is both equilateral and equiangular.

Example of regular polygon

Formula

Interior angle of regular polygon = (n-2) × 180°

or = (n-2) × π radian

Square is a regular polygon as its sides are equal and all angles are equal.

Irregular polygon

A polygon which is not a regular polygon, i.e. not an equiangular and equilateral is called irregular polygon.

Example of irregular polygon

A rectangle is an irregular polygon.

Simple polygon

It is a flat shape consisting of straight and non intersecting line segments that are joined to form a single close path. A Simple Polygon does not cross over itself. It is also called Jordan Polygon. All convex polygons are simple.

Example of simple polygon

Types based on number of sides

Table of polygons with number of sides and angles
Number of sides of polygon	Name of polygon	Number of angles of polygon
3	Triangle	3
4	Quadrilateral	4
5	Pentagon	5
6	Hexagon	6
7	Heptagon	7
8	Octagon	8
9	Nonagon	9
10	Decagon	10

Learn Frequently Asked Questions

What is a polygon?

A closed plane figure formed by line segments and two line segments which intersect at only their end points.

What is the sum of the angles of a polygon?

The sum of angles of a polygon with n sides is (n-2)180⁰.

What is the sum of exterior angles of a polygon?

The sum of exterior angles of the polygon is 360⁰.

Is an equilateral triangle a regular polygon?

Yes, an equilateral triangle is a regular polygon as its all sides are equal and all its angles are equal.

Is a rectangle a regular polygon also?

No, a rectangle is not a regular polygon as its angles are equal but all sides are not equal.

Practice With Solved Examples

Find the number of sides of a polygon if each of its interior angles is 140⁰.

Let number of sides of polygon = n

Each interior angle = $\frac{(n - 2) 180}{n}$

140 = $\frac{(n - 2) 180}{n}$

140n = 180n - 360

360 = 180n - 140n

360 = 40n

$\frac{360}{40} = n$

n = 9

Find the number of sides of regular polygon if each exterior angle is 40⁰

Sum of all exterior angle = 360⁰

Each exterior angle = 40⁰

Number of exterior angles = $\frac{360}{40}$

Number of exterior angles = 9

∴ Number of sides of polygon = 9

If each interior angle of a regular polygon is 150⁰ then find its exterior angle.

Each interior angle = 150⁰.

We know that, interior angles + exterior angles = 180⁰

150⁰ + exterior angles = 180⁰

exterior angles = 180⁰ - 150⁰

exterior angles = 30⁰

The ratio between exterior angle and interior angle of a regular polygon is 1:5. Find its interior angle.

Let exterior angle and interior angle be x and 5x respectively.

Also, interior angles + exterior angles = 180⁰

5x + x = 180⁰

6x = 180⁰

x = $\frac{180}{6}$

x = 30⁰

∴ exterior angle = 30⁰

interior angle = 5x = 5 × 30⁰

i.e. interior angle = 150⁰

Fill in Blanks Worksheets

Total - 2

Worksheet

Help box

540°

180°

1080°

equilateral

diagonal

360°

angles

In a regular polygon all sides and all ___ are equal.
___ triangle is a regular polygon.
A triangle has no ___ .
The sum of exterior angles of a polygon is ___ .
Concave polygons have at least one angle more than ___ .
The sum of interior angles of a pentagon is ___ .
The number of sides of a polygon must be greater than or equal to ___.
The sum of interior angles of an eight sided polygon is ___ .
A regular hexagon has ___ diagonals.
A polygon whose sum of interior angles is 1440° has ___ sides.

Blanks PDF worksheet

26.5 KB

Worksheet

Fill blanks with the number of sides or sum of interior angles of polygon.

S.N.	Number of sides of polygon	Sum of interior angles of the polygon
1)	12	___
2)	___	1620°
3)	10	___
4)	___	1800°
5)	5	___

Blanks PDF worksheet

25.4 KB

Write True or False Worksheet

A square is a regular polygon.
A triangle has three diagonals.
Sum of interior angles of a regular hexagon is 720°
A n-sided convex polygon has $\frac{n (n - 3)}{2}$ diagonals.
The right angled triangle is a regular polygon.
In convex polygons each angle is less than 180°.
A heptagon has eight sides.
Each interior angle of a nonagon is 140°.
The number of sides in a polygon must be a whole number.
A decagon has 35 diagonals.

True False PDF worksheet

30.5 KB

Match Columns Worksheet

Name of polygon		Number of sides of polygon
1)	Pentagon	a)	7
2)	Octagon	b)	9
3)	Triangle	c)	10
4)	Heptagon	d)	6
5)	Nonagon	e)	5
6)	Decagon	f)	8
7)	Hexagon	g)	3

Matching PDF worksheet

19.9 KB

Multiple Choice Questions Worksheet

1) A polygon with 5 sides is called as

hexagon
decagon
pentagon
nonagon

2) A polygon with 8 sides is called as

hexagon
heptagon
octagon
decagon

3) In convex polygon, each angle of polygon is

= 90⁰
= 180⁰
< 90⁰
< 180⁰

4) In concave polygon, at least one angle of polygon is

< 90⁰
< 180⁰
> 90⁰
> 180⁰

5) A polygon is said to be regular polygon, if all of its

interior angles are equal
exterior angles are equal
sides are equal
all of these

6) At each vertex of polygon, the sum of interior angle and exterior angle is equal to

90⁰
180⁰
270⁰
360⁰

7) The regular polygon with three sides is a

isosceles triangle
equilateral triangle
scalene triangle
rhombus

8) The least number of sides in a polygon is

9) The sum of interior angles of a polygon with 7 sides is

900°
800°
700°
540°

10) If the sum of interior angles of a polygon is 1440° then the number of sides of the polygon are

MCQ PDF worksheet

29 KB

MCQs Answer Keys