Types of Polygons: Definition, Formulas, Solved Examples

Types of Polygons: A Polygon is a flat two-dimensional closed figure made up of line segments. The word Polygon is derived from the Greek language, where ‘poly’ means many and ‘gonna’ means angles. A Polygon is made up of only straight lines. Each straight line in a Polygon is called its side.

A Polygon is classified based on its sides like a triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, and decagon according as it contains (3, 4, 5, 6, 7, 8, 9) and (10) sides, respectively. In this article, the various types of polygons with definition, their components etc., are discussed. Read on to know more.

Definition of Polygons

A rectilinear shape bounded by three or more sides is called a Polygon. The number of sides is equal to the number of angles in a Polygon. In the following paragraphs, you will find the types of Polygons with definition. We have also included types of polygons images.

Types of Polygons Based on Side Length

Types of Polygons and their properties are given below. There are two types of Polygons and their names classified based on their side lengths are:

1. Regular Polygon
2. Irregular Polygon

1. Regular Polygon

A Regular Polygon is a Polygon in which all the sides are of the same length. This makes the regular polygon both equiangular and equilateral.
Example: Equilateral Triangle and Square.

2. Irregular Polygon

An Irregular Polygon is a Polygon with different side lengths.
Examples: Rectangle and Rhombus.

Types of Polygons Based on Their Interior Angles

There are two types of polygons classified based on their interior angles. These are:

1. Concave Polygon
2. Convex Polygon

1. Concave Polygon

A polygon in which at least one angle is more than ({rm{18}}{{rm{0}}^{rm{o}}}) is called a concave polygon. In a concave polygon, some sides go inside the polygon when extended. In the given figure, (ABCD) is a concave polygon. Clearly, reflex (∠C) is more than ({rm{18}}{{rm{0}}^{rm{o}}}) as shown in the figure. This indicates that a concave polygon having an interior angle of more than ({rm{18}}{{rm{0}}^{rm{o}}}.)

2. Convex Polygon

A convex polygon is a polygon whose interior angles are smaller than a straight angle.
In a convex polygon, no side goes inside the Polygon when extended.
In the given figure, (PQRS) is a Convex Polygon.

Here, in this article, by a Polygon, we would mean a Convex Polygon only. In a Convex Polygon, the vertices are always outwards.

Equilateral Polygon

A Polygon is said to be equilateral if all its sides are equal.

Example: Equilateral Triangle, Square, Rhombus.

Equiangular Polygon

A Polygon is said to be equiangular if all its angles are equal.

Example: Equilateral Triangle and Square

Types of Polygons and Sides

The straight lines that form the Polygon are called Polygon’s edges or sides. And, the corner or the point where any two sides meet is called the vertex of the Polygon. Based on the number of sides and angles, polygons are classified into different types.

Some of the different types of Polygons based on the number of sides and angles are given below.

1. Triangle (Trigon)

Triangle is a polygon that has three sides. These trigons or triangles are further classified into different categories, such as:

• Scalene Triangle: A triangle with all three sides different in lengths is called a scalene triangle.
• Isosceles Triangle: A triangle in which two sides are of equal lengths is called an isosceles triangle.
• Equilateral Triangle: A triangle with all three sides equal is called an Equilateral triangle. And, all angles of an equilateral triangle measures ({rm{6}}{{rm{0}}^{rm{o}}})

The sum of the interior angle of a triangle is ({rm{18}}{{rm{0}}^{rm{o}}}).

2. Quadrilateral

The quadrilateral is a four-sided polygon or a quadrangle. The different types of quadrilateral Polygon are square, rectangle, rhombus, parallelogram and kite.The sum of the interior angle of a quadrilateral is ({rm{36}}{{rm{0}}^{rm{o}}})

3. Pentagon

Pentagon is a five-sided Polygon. A pentagon is a figure obtained by joining the points of five-line segments in the same plane. 

A regular pentagon has all five sides of the Polygon equal in length. If the length of the sides is not equal, then it is called an irregular pentagon.The sum of the interior angle of a pentagon is ({rm{54}}{{rm{0}}^{rm{o}}})

4. Hexagon

A hexagon is a Polygon that has (6) sides and (6) vertices. A regular hexagon has all six sides equal in length. And, its interior angles and exterior angles are also equal in measure. The sum of the interior angle of a hexagon is ({rm{72}}{{rm{0}}^{rm{o}}}.)

Types of Polygons with Sides 3-20

Formulas on Polygons

Following are the different types of polygons and their formula:

1. The formula to find the sum of interior angles of a Polygon with (“n”) sides = (n – 2){180^{rm{o}}})

2. The formula to find the number of diagonals of a Polygon with (“n”) sides = frac{{left( {n – 3} right)n}}{2}.)

3. The formula to measure all the interior angles of a regular (“n)-sides(”) Polygon = frac{{(n – 2){{180}^{rm{o}}}}}{n})

4. The sum of all the exterior angles in any polygon taken in order is ({{{360}^{rm{o}}}})

5. The formula to measure each of the exterior angles of a regular (“n)-sides (”) Polygon = frac{{{{360}^{rm{o}}}}}{n})

Other important Maths Formulas:

Types of Polygons Worksheet       

The experts at Embibe have curated types of polygons worksheet for you to score the highest marks possible.

Q.1. Write the number of sides in a pentagon.
Ans: Pentagon is a Polygon consisting of 5 sides.

Q.2. What is the measure of all the angles in a square?
Ans: We know square is a Regular Polygon with each angle measures \({90^{\rm{o}}}.\)
Therefore, the sum of four angles in a square is:
({90^{rm{o}}} + {90^{rm{o}}} + {90^{rm{o}}} + {90^{rm{o}}} = {360^{rm{o}}})
Therefore, the sum of the measure of all the angles of a square is ({360^{rm{o}}})

Q.3. If the sum of all interior angles of a Polygon is \({3240^{\rm{o}}},\) how many sides does the Polygon have?
Answer: We know the formula to find the sum of interior angles of a Polygon with (“n”\) sides \( = (n – 2){180^{\rm{o}}}.\)
\( \Rightarrow {3240^{\rm{o}}} = (n – 2){180^{\rm{o}}}\)
\( \Rightarrow (n – 2) = \frac{{{{3240}^{\rm{o}}}}}{{{{180}^{\rm{o}}}}} = 18\)
\( \Rightarrow (n – 2) = 18\)
\( \Rightarrow n = 18 + 2\)
\( \Rightarrow n = 20\)
Therefore, the Polygon has \(20\) sides.

Q.4. How many sides does a Polygon have if the sum of the interior angles is \({540^{\rm{o}}}?\)
Ans: From the given, the sum of the interior angles is \({540^{\rm{o}}}.\)
The formula to measure all the interior angles of a regular “n-sides” Polygon \( = \frac{{(n – 2){{180}^{\rm{o}}}.}}{n}\)
\( \Rightarrow {540^{\rm{o}}} = (n – 2){180^{\rm{o}}}\)
\( \Rightarrow (n – 2) = \frac{{{{540}^{\rm{o}}}}}{{{{180}^{\rm{o}}}}} = 3\)
\( \Rightarrow (n – 2) = 3\)
\( \Rightarrow n = 3 + 2\)
\( \Rightarrow n = 5\)
Therefore, the Polygon has \(5\) sides.

Q.5. Find the interior angle of a Regular Polygon of \(12\) sides.
Ans: We know from the given number of sides \(n=12\)
The formula to measure all the interior angles of a regular \(“n-\)sides\(”\) Polygon \( = \frac{{(n – 2){{180}^{\rm{o}}}}}{n}\)
The interior angle of the Regular Polygon \( = \frac{{(12 – 2){{180}^{\rm{o}}}}}{{12}}\)
The interior angle of the Regular Polygon \( = \frac{{10 \times {{180}^{\rm{o}}}}}{{12}}\)
The interior angle of the Regular Polygon \({ = {{150}^{\rm{o}}}}\)
Therefore, the interior angle of the Regular Polygon is \({{{150}^{\rm{o}}}.}\)

Q.6. If the sum of the interior angles of a Polygon is \(6\) straight angles, how many sides have the Polygon?
Ans: We know the formula to find the sum of interior angles of a Polygon with \(“n”\) sides,
\({\rm{ = }}\left( {n – 2} \right)\) straight angles.
\( \Rightarrow \left( {n – 2} \right) = 6\)
\( \Rightarrow n = 6 + 2\)
\( \Rightarrow n = 8\)
Therefore, the Polygon has 8 sides.

Summary

A rectilinear shape bounded by three or more sides is called a polygon. The straight lines that make the Polygon are known as the polygon’s sides or edges. At the same time, the corner or the point where any two sides meet is called the vertex of the polygon. On the number of sides and angles, polygons are classified into different types. A three-sided polygon is a triangle, and a four-sided polygon is a quadrilateral etc.

FAQs on Types of Polygon

Following are the frequently asked questions on Polygon:

Q1. What is a \(27-\)sided Polygon called?
Ans: \(27\) sided polygon called icosiheptagon.

Q2. What is a \(10-\)sided Polygon called?
Ans: \(10\) sided polygon called a decagon.

Q3. What are the \(10\) types of polygons?
Ans: \(10\) Types of Polygons based on sides are:
1. Triangle \(–3\) sides
2. Quadrilateral \(–4\) sides
3. Pentagon \(–5\) sides
4. Hexagon \(–6\) sides
5. Heptagon \(–7\) sides
6. Octagon \(–8\) sides
7. Nonagon \(–9\) sides
8. Decagon \(–10\) sides
9. Hendecagon \(–11\) sides
10. Dodecagon \(–12\) sides

Q4. What are the types of Regular Polygons?
Ans: A polygon having all sides equal and all angles equal is called a regular polygon.
Types of regular polygons are:
1. Equilateral triangle
2. Square
3. Pentagon
4. Hexagon
5. Octagon

Q5. What is a \(100-\)sided shape?
Ans: \(100\) sided Polygon called hectogon.

Q6. What are concave polygons?
Ans: A polygon in which at least one angle is more than \({\rm{18}}{{\rm{0}}^{\rm{o}}}\) is called a concave polygon. In a concave polygon, some sides go inside the polygon when extended.

Q7. What are the types of polygons based on side length?
Ans: There are two Types of Polygons classified based on their side lengths are,
1. Regular Polygons: A Regular Polygon is a Polygon that is both equiangular and equilateral.
Examples: Equilateral Triangle and Square
2. Irregular Polygons: Irregular Polygons are polygons that are not regular.
Examples: Rectangle and Rhombus

Q8. Are circles polygons?
Ans: Circles are formed with curved lines, and they do not have sides. So, circles are not polygons.

This article helps to learn in detail about the types of Polygons based on their number of sides. If you have any queries please reach out to us in the comments down below.

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