What are Polygons?
- A Polygon is a closed figure made up of lines segments (not curves) in two-dimensions.
- A minimum of three line segments are required for making a closed figure, thus a polygon with a minimum of three sides is known as Triangle.
By definition, we know that the polygon is made up of line segments. Below are the shapes of some polygons that are enclosed by the different number of line segments.
Depending on the sides and angles, the polygons are classified into different types, namely:
- Regular Polygon
- Irregular Polygon
- Convex Polygon
- Concave polygon
If all the sides and interior angles of the polygon are equal, then it is known as a regular polygon.
If all the sides and the interior angles of the polygon are of different measure, then it is known as an irregular polygon.
If all the interior angles of a polygon are strictly less than 180 degrees, then it is known as a convex polygon. The vertex will point outwards from the centre of the shape.
If one or more interior angles of a polygon are more than 180 degrees, then it is known as a concave polygon. A concave polygon can have at least four sides. The vertex points towards inside of the polygon.
However, a number of polygons are defined based on the number of sides, angles and their properties. Let us see one of the frequently used and the primary type of polygon, i.e. triangle.
Classification of Triangles
In our article on Geometric Shapes, we discussed the polygons with the least number of sides – the Triangle. In this section, you will go through different types of triangles.
- Equilateral triangle – Having all sides equal.
- Isosceles triangle – Having any 2 sides equal.
- Scalene triangle – Has 3 unequal sides.
- Acute angled Triangle– Each angle is less than 900
- Right Angled Triangle– Any one angle is 900
- Obtuse Angled Triangle– Any one angle is greater than 900
|An interesting fact about the Triangle:
A Quadrilateral is a polygon having the number of sides equal to four. That means, a polygon formed by enclosing four line segments such that they meet at each other at corners to make 4 vertices.
The table below gives the comparison of Opposite sides, angles, and diagonals of different Quadrilateral.
|Quadrilateral||Opposite||Sides||All sides Equal||Opposite angles equal||Diagonal||Diagonal|
(Only one side)
Polygon: A general comparison
|Polygon||No. of Sides||No. of Diagonal||No. of vertices||Interior Angle|
Polygon angle sum
As we know, any polygon has as many vertices as it has sides. Each corner has a certain measure of angles. These angles are categorized into two types namely interior and exterior angles of a polygon.
The sum of all the interior angles of a simple n-gon = (n − 2) × 180°
= (n − 2)π radians
Where ‘n’ is equal to the number of sides of a polygon.
For example, a quadrilateral has four sides, therefore, the sum of all the interior angle = (4 – 2) × 180°
= 2 × 180°
The sum of interior and the corresponding exterior angles at each vertex of any polygon are supplementary to each other.
There are several formulas defined for polygons based on the number of sides.
As we have already given that the sum of all the interior angles of an n-sided polygon is (n – 2) × 180°.
The number of diagonals in a polygon with n sides = n(n – 3)/2
The number of triangles formed by joining the diagonals from one corner of a polygon = n – 2
The measure of each interior angle of n-sided regular polygon = [(n – 2) × 180°]/n
The measure of each exterior angle of an n-sided regular polygon = 360°/n
Three Dimensional Shape (3-D shape)
A three-dimensional shape is a solid object that is formed by a combination of polygons and 2d shapes. Some of the 3d shapes which we can observe in real-life are:
- These are the shapes that can be projected on a piece of paper but cannot be drawn on a paper. These shapes are known as solids.
|2-D shape (Polygon)||3-D Shape|
- 3-D shapes have faces as the distinguishing feature.
To know more about polygons, types of polygons and 3-D shapes, download BYJU’S – The Learning App.
Frequently Asked Questions – FAQs
What is a polygon?
What is called a polygon with 7 sides?
What is called a polygon with 9 sides?
How many diagonals does a polygon have?
What are the different types of polygons?
Regular polygon – all the sides and measure of interior angles are equal
Irregular polygon – all the sides and measure of interior angles are not equal, i.e. different
Convex polygon – all the interior angles of a polygon are strictly less than 180 degrees. The vertex will point outwards from the centre of the shape
Concave polygon – one or more interior angles of a polygon are more than 180 degrees. A concave polygon can have at least four sides. The vertex points towards inside of the polygon.