Types of Polygon
A polygon is a two-dimensional closed figure which has at least three straight sides, three angles, and three vertices. The term 'Poly' means many and the term 'gon' refers to angle. For example, a triangle has three sides, three vertices, and three angles. So it can be termed as a polygon. There are many types of polygons. The classification of polygons is made on the basis of the number of angles, their sides, and also according to whether a polygon is regular or irregular.
What are the Different Types of Polygons?
A polygon is a closed shape. There can be any number of sides and angles for a polygon. Some important terms associated with polygons are vertices, edges, and diagonals. The sides of a polygon are called edges, the point at which two edges of a polygon meet are called vertices, and a line segment joining two opposite vertices of a polygon is called a diagonal. Polygons can be classified based on the number of sides and the angles. The polygons are classified on the basis of:
- Number of sides
- Angles (Concave or Convex Polygons)
- Measurement of sides and angles (Regular or Irregular Polygons)
- The boundary of the polygons (Simple or Complex Polygons)
Let us look at the types of polygons.
Types of Polygons Based on the Number of Their Sides
A polygon has a minimum of 3 sides and angles. The table shown below lists 10 polygons and their description based on their number of sides. A polygon that has more than 20 sides is referred to as 'n-gons'. There is no specific name for a polygon that has more than 20 sides. It is generally called 'A polygon with n sides.
There are polygons that have more than 15 sides also. Polygons that have more than 20 sides are called n-gons.
Types of Polygons Based on Their Angles
A polygon can also be classified based on the angles formed by the adjacent sides of a polygon. The measure of the angle may be less than 180° or more than 180°. Based on this, the polygons are classified as convex polygons and concave polygons. The interior angles of an 'n' sided polygon are given by the formula ((n-2)180°)/n.
Convex polygons
These polygons have the measure of their interior angles to be always less than 180°. A regular hexagon, which has 6 sides can be termed a convex polygon. Also, the vertices of the convex polygon are protruding or pointing outwards.
Concave polygons
They are the opposite of convex polygons, in which at least one of the interior angles measure more than 180°. Also, in a concave polygon, the vertices can be pointing both inwards and outwards.
The figure given below shows a convex and a concave polygon.
Types of Polygons Based on the Measurement of Sides and Angles
A polygon need not necessarily always have the same measurement of sides and angles. Thus, polygons can be differentiated on the basis of the measurement of sides and angles. They are classified as:
Regular Polygon
A polygon that has all equal sides and angles is called a regular polygon. In other words, regular polygons are equilateral and equiangular. For example, a square has all of its four sides to be equal and all of its angles are equal to 90°, so a square is an example of a regular polygon.
Irregular Polygon
An irregular polygon is a figure that has unequal sides and unequal angles. For example, a rectangle has all of its angles equal to 90° but all four sides are not equal. So it can be termed as an irregular polygon.
Types of Polygons Based on the Boundary of Polygon
A polygon may or may not intersect on the boundary. Thus, the types of polygons on the basis of the boundary of the polygon are given as:
Simple Polygons
A simple polygon is a polygon that does not intersect itself. A simple polygon consists of one boundary.
Complex Polygons
A polygon that intersects itself and has more than one boundary is called a complex polygon.
Topics Related to Types of Polygons
Check out some interesting articles related to types of polygons.
Solved Examples on Types of Polygon
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Example 1: Write down the number of sides of the polygons shown in the figure and classify them based on their sides and angles.
Solution: The first figure has 7 sides, all of which are not equal and we can observe that two of the vertices point inwards, which means two of the interior angles are greater than 180°. So this polygon is classified as a concave irregular polygon.
The second figure has 5 sides, all of which are equal and we can observe all of the vertices point outwards, which means all the angles are less than 180°. So this polygon is classified as a convex regular polygon. And since it has 5 sides, it is called a pentagon.
The third figure has 4 sides, all of which are not equal and we can observe all of the vertices point outwards, which means all the interior angles are less than 180°. So this polygon is classified as a convex irregular polygon.
FAQs on Types of Polygon
What are the Types of Polygon?
A polygon is a two-dimensional closed shape that is made by three or more line segments. Thus, polygons can be categorized on the basis of different criteria which are:
- The number of sides
- Angles (Concave or Convex Polygons)
- Measurement of sides and angles (Regular or Irregular Polygons)
- The boundary of the polygons (Simple or Complex Polygons)
All polygons can be categorized into different types of polygons based on the respective criteria they follow.
What are all the Different Types of Polygons?
The different types of polygons are:
- Concave polygons (at least one of the interior angles is greater than 180°)
- Convex polygons (all the interior angles are less than 180°
- Regular polygons (all the sides and angles measure the same)
- Irregular polygons (all the sides and angles measure different)
- Simple polygons (polygon does not intersect itself)
- Complex polygons (polygon intersects itself)
What are the Types of Polygons Based on the Number of Sides?
Polygons are closed figures which have at least three straight sides and angles. Based on the number of sides, polygons have been given names. For example, a polygon with three straight sides is a triangle, and a polygon with four equal sides and angles in a square.
What is the Difference Between Convex and Concave Type of Polygons?
Convex and concave polygons are types of polygons that differ based on their interior angles. A convex polygon has interior angles less than 180°, whereas, a concave polygon has at least one interior angle greater than 180°. A convex polygon has all its vertices pointing outwards, whereas a concave polygon has at least one of its vertices pointing inwards.
What Types of Polygons are Square and Rectangle?
Square and rectangle are simple, convex polygons, and quadrilaterals as their boundaries do not intersect each other, their interior angles are lesser than 180° and they have four sides respectively. The square is a regular polygon while the rectangle is an irregular polygon.
Which Type of Polygon has Seven Sides?
The type of polygon that has seven sides is referred to as Heptagon. It is made of two words, "Hepta" which means seven, and "gon" which means angles thereby meaning that it is a seven-sided shape having seven angles.
Is Equilateral Triangle a Convex Type of Polygon?
Yes, an equilateral triangle is a convex type of polygon as interior angles of an equilateral triangle are always 60° which is lesser than 180°. The value of the interior angle of the equilateral triangle always remains 60° and never increases thereby proving it to be a convex polygon.
What Type of Polygon is a Trapezoid?
A trapezoid is a simple, convex polygon and a quadrilateral as it has only one boundary, with interior angles lesser than 180° and has four sides respectively. It is also an irregular polygon as the length of all its sides and angles do not measure the same.