Concave Polygon

What is a Concave Polygon? 

A polygon that has one or more interior angles greater than 180 degrees is known as Concave Polygon.

A polygon is a two-dimensional closed figure made up of line segments that are in the same plane. 

A polygon has another name called a polyhedron. An n-gon is a polygon with n sides. The point where two line segments meet is called polygon's vertices. The exterior angles of a polygon always sum 360°.

Types Of Polygons

On the basis of the regularity of sides, they are classified as 

  1. Regular polygons 

  2. Irregular polygons

On the basis of shape, they are classified as 

  1. Convex polygons

  2. Concave polygons

Regular Polygons — These are the polygons that have the same length of all sides. 

Example: Square, equilateral triangle, etc.

Irregular Polygons — These are the polygons in which the lengths of sides are not equal. As the name suggests these are irregular polygons.

Example: Rectangle, scalene triangle, etc.

Difference Between Concave And Convex Polygons

Consider these two polygons. A concave or a convex polygon can be regular or irregular. We are mainly concerned here about the shape, not about the lengths of sides.

A simple definition of these two can be as follows 

Convex Polygons 

In this type of polygon all the interior angles are less than 180°.  A triangle is always convex polygon no matter which triangle it is.

Concave Polygons

In this type of polygon one or more of the interior angle is more than 180°. Remember a triangle can never be a concave polygon as the sum of all interior angles is itself 180°. It has at least one vertex that points inwards in order to give it a concave shape. At least one of the interior angles is greater than 180° but less than 360°.


In the above figures if we extend all the line segments on both sides we get something like this.

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If the extended line segments do not meet in the interior part of the polygon then it is there as a convex polygon.

And if the extended line segments meet in the interior part of the polygon then it is termed as a concave polygon.

All stars are termed as concave polygons as they have vertices which are pointing inwards. All concave polygons are classified as irregular.

Applications Of Polygons In Nature

Polygons are used in mathematical geometry to study about different shapes. In crystal formation unit cells are used as their building blocks can also be termed as polygons. Polygons find their use in engineering drawings, graphics, etc.

FAQ (Frequently Asked Questions)

1. What is the Difference Between Concave and Convex Polygons?

Answer: In a convex polygon, all the interior angles are less than 180° while a concave polygon has one or more interior angles that are greater than 180°.

2. How To Calculate The Area Of A Concave Polygon?

Answer: You can easily do it by finding various simple shapes inside the concave polygon then finding the area of each individual shape using their formulas and then adding them.

3.How To Calculate The Perimeter Of Concave Polygons? 

Answer: Perimeter in simple terms is the sum of the length of all sides. In a concave polygon, you can calculate the lengths of all different sides and then add them together.