What are the Different Classifications of Polygons?

In Geometry, we have learned different types of two-dimensional shapes and three-dimensional shapes. We know that 2D shapes have only two dimensions: length and breadth, whereas 3D shapes have three dimensions: length, breadth, and height. The shapes can be made up of straight lines, curves, points, lines, angles, etc. A shape that is made up of straight lines in a two-dimensional plane is called polygon. In other words, a polygon is defined as a two-dimensional closed figure made up of at least three line segments. Consider an example, a circle is a 2D shape. As it is made of curved lines, a circle is not considered as a polygon.

 

Based on the number of sides, the polygons are classified into different types. The polygons with the least number of sides are triangles. The three-line segments are connected end to end to form the closed figure. Likewise, the polygons with “n” number of sides are called “n-gons”.

Some other classifications of the polygon, based on the number of sides are:

 

Quadrilateral: A polygon with four sides is called a quadrilateral. Some of the examples of quadrilaterals are square, rhombus, rectangle, parallelogram, etc.

Pentagon: A polygon with a total of 5 straight line segments is called a pentagon. It has 5 vertices. One good example of a pentagon is a black section on a soccer ball.

Hexagon:  A shape that is made up of six-line segments is called a hexagon. It has six sides, six vertices and six angles.

Heptagon: Heptagon, also called 7-gon, is a seven-sided polygon with 7 vertices and 7 angles.

 

The other classification of polygons is based on the measurement of angles and the sides of the polygon. They are:

Regular and Irregular Polygons

If all the interior angles and the sides of a polygon are of the same measurements, it is called a regular polygon. An example of a regular polygon is square. If the measure of interior angles and sides of a polygon varies, it is considered an irregular polygon. Examples of irregular polygons include rectangle, scalene triangle, etc.

Convex and Concave Polygons

A convex polygon is a polygon in which all the interior angles are strictly less than 180°. Also, the vertices are pointing outwards from the centre of the shape. Whereas in a concave polygon, at least one interior angle measures greater than 180°, and certain diagonals lie outside of the polygon.

Simple and Complex Polygon

A polygon with only one boundary and it does not intersect itself is called a simple polygon.  whereas the complex polygon intersects itself.

 

The area and perimeter of the polygons are calculated using the sides of a polygon. For example, if all sides of a triangle are known, its area can be calculated using Heron’s formula. Similarly, the perimeter of a regular polygon can be calculated based on the number of sides. We can calculate the perimeter by multiplying the number of sides of a polygon by the polygon’s side length.

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