# How to Find Sides of a Polygon – Definition, Examples, Facts, FAQs

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## What Are Sides of a Polygon?

The sides of a polygon are the straight line segments that form the outer boundary of the polygon. Each side connects two consecutive vertices (corners) of the polygon.

The sides of a polygon are also called its edges. The points where two sides meet are the vertices (or corners) of a polygon.

## What Are Polygons?

In geometry, a polygon can be defined as a flat or two-dimensional closed shape bounded with straight sides. It does not have a curved boundary. At least 3 straight line segments (sides) are required to form a polygon.

Here are a few examples of polygons.

Here are a few non-examples of a polygon.

## Sides of a Polygon: Definition

Sides of a polygon are the line segments that define the boundary of the polygon.

## Classification of Polygons Based on the Number of Sides

We can classify polygons based on the number of sides. The minimum number of sides required to make a polygon is 3.

## Types of Polygons Based on Sides

Let’s discuss types of polygons based on different criteria.

• Simple and Complex Polygons:

This classification is done depending whether the sides cross themselves or not.

• Regular and Irregular Polygons

This classification is done on the basis of the measurements of sides and angles.

## How to Find the Number of Sides of a Polygon

The number of sides in a polygon can vary, and different polygons have different shapes and side lengths. For example, a triangle has three sides, a quadrilateral has four sides, and a pentagon has five sides, etc.

• Number of sides of a polygon given the sum of interior angles

Sum of interior angles $= (n \;-\; 2) \times 180^{\circ}$

where

n is the number of sides.

Example: If the sum of interior angles of a polygon is 180, find the number of sides.

$180^{\circ} = (n – 2) \times 180^{\circ}$

$\Rightarrow 1 = n – 2$

$\Rightarrow n = 3$

• Number of sides of a “regular polygon” given the measure of an interior angle

Each interior angle of a regular polygon $= \frac{(n – 2) \times 180^{\circ}}{n}$,

where

n is the number of sides.

Example: If each interior angle of a polygon is 90, find the number of sides.

$\Rightarrow 90^{\circ} = \frac{(n – 2) \times 180^{\circ}}{n}$

$\Rightarrow \frac{90^{\circ}}{180^{\circ}} \times n = n – 2$

$\Rightarrow \frac{n}{2} = n – 2$

$\Rightarrow n – \frac{n}{2} = 2$

$\Rightarrow \frac{n}{2} = 2$

$\Rightarrow n = 4$

• Number of sides of a regular polygon when given the measure of an exterior angle

To find the number of sides of a polygon when the exterior angle is given, we use the formula:

Measure of an exterior angle of a regular polygon $= \frac{360^{\circ}}{n}$

where

n is the number of sides.

Example: If each exterior angle of a polygon is 36, find the number of sides.

$36^{\circ} = \frac{360^{\circ}}{n}$

$\Rightarrow n = 10$

## Facts about Sides of a Polygon

• The number of interior angles of a polygon are equal to the number of sides present.
• Diagonals of a polygon are line segments that connect two non-adjacent vertices.

## Conclusion

In this article, we learned about the sides in a polygon, an essential part of a polygon. Sides of a polygon are the line segments that form the boundary. Let’s solve a few examples and practice MCQs for better comprehension.

## Solved Examples on Sides of a Polygon

1. How many sides are there in the following figure?

Solution:

The number of sides in the above polygon are 8.

Let’s name the vertices.

The 8 sides are:

AB, BC, CD, DE, EF, FG, GH, and AH.

2. Find the number of sides when the sum of interior angles of a polygon is $1080^{\circ}$.

Solution:

Sum of interior angles of a polygon $= (n – 2) \times 180^{\circ}$

where

‘n’ is the number of sides

Thus, $1080^{\circ} = (n – 2) \times 180^{\circ}$

$n – 2 = \frac{1080^{\circ}}{180^{\circ}}$

$n – 2 = 6$

$n = 8$

3. Find the number of sides of a regular polygon when each interior angle is $60^{\circ}$.

Solution:

Each interior angle of a regular polygon $= \frac{(n – 2) \times 180^{\circ}}{n}$

$60^{\circ} = \frac{(n – 2) \times 180^{\circ}}{n}$

$\frac{60^{\circ}}{180^{\circ}} n = n – 2$

$\frac{n}{3} = n – 2$

$2 = n – \frac{n}{3}$

$2 = \frac{3n – n}{3}$

$2 = \frac{2n}{3}$

$n = 3$

4. Identify regular and irregular polygons: Square, Rhombus, Equilateral Triangle, Rectangle.

Solution:

Square and equilateral triangle are regular polygons.

Rectangle and rhombus are irregular polygons.

Rectangle has equal interior angles, but non-equal sides.

Rhombus has equal sides, but non-equal angles.

6. Find the number of sides of a polygon when the interior angle sum is $1440^{\circ}$.

Solution:

$1440^{\circ} = (n – 2) \times 180^{\circ}$

$n – 2 = \frac{1440^{\circ}}{180^{\circ}}$

$n – 2 = 8$

$n = 8 + 2 = 10$

7. Name a regular polygon whose each interior angle is $162^{\circ}$.

Solution:

Each interior angle of a regular polygon $= \frac{(n – 2) \times 180^{\circ}}{n}$, where “n” represents the number of sides.

$162^{\circ} = \frac{(n – 2) \times 180^{\circ}}{n}$

$\frac{162^{\circ}}{180^{\circ}} n = n – 2$

$\frac{9}{10}n = n – 2$

$2 = n – \frac{9n}{10}$

$2 = \frac{10n – 9n}{3}$

$2 = \frac{n}{10}$

$n = 20$

The polygon is a regular 20-gon (also called regular icosagon).

## Practice Problems on Sides of a Polygon

1

### Which polygon has 6 sides?

Heptagon
Nonagon
Decagon
Hexagon
CorrectIncorrect
A hexagon has 6 sides.
2

### A polygon with 9 sides is called ____.

Heptagon
Nonagon
Decagon
Hexagon
CorrectIncorrect
A nonagon has 9 sides.
3

### The polygon with equal number of sides and angles is called

Regular Polygon
Irregular Polygon
Convex Polygon
Simple Polygon
CorrectIncorrect
A regular polygon has an equal number of sides and angles.
4

### A polygon whose sides cross each other is called

Irregular polygon
Complex polygon
Concave polygon
Simple polygon
CorrectIncorrect
A complex polygon has self-intersecting sides.
5

### The number of sides of a regular polygon when the exterior angle is $30^{\circ}$ is:

20
15
12
8
CorrectIncorrect
Each exterior angle $= 30^{\circ}$
Number of sides $= n = \frac{360^{\circ}}{30^{\circ}} = 12$
6

### Which polygon has the sum of interior angles $= 540^{\circ}$?

Triangle
Pentagon
Heptagon
CorrectIncorrect
Sum of angles $= 540^{\circ}$
$540^{\circ} = (n - 2) \times 180^{\circ}$
$n - 2 = \frac{540^{\circ}}{180^{\circ}}$
$n - 2 = 3$
$n = 3 + 2 = 5$
The polygon is pentagon.