Polygons

The simple closed curves which are made up of line segments only are called the Polygons.

Classification of Polygons

Polygons can be classified by the number of sides or vertices they have.

Number of sidesName of PolygonFigure
3TriangleThis image has an empty alt attribute; its file name is image-3.png
4QuadrilateralThis image has an empty alt attribute; its file name is image-4.png
5PentagonThis image has an empty alt attribute; its file name is image-5.png
6HexagonThis image has an empty alt attribute; its file name is image-6.png
7HeptagonThis image has an empty alt attribute; its file name is image-7.png
8OctagonThis image has an empty alt attribute; its file name is image-8.png
9NonagonThis image has an empty alt attribute; its file name is image-9.png
10DecagonThis image has an empty alt attribute; its file name is image-10.png
nn-gon  

Diagonals

Any line segment which connects the two non-consecutive vertices of a polygon is called Diagonal.

Convex and Concave Polygons

The polygons which have all the diagonals inside the figure are known as a Convex Polygon.

The polygons which have some of its diagonals outside the figure also are known as a Concave Polygon.

Regular and Irregular Polygons

Polygons which are equiangular and equilateral are called Regular Polygons i.e. a polygon is regular if –

  • It’s all sides are equal.
  • It’s all angles are equal.

square is a regular polygon but a rectangle is not as its angles are equal but sides are not equal.

Angle Sum Property

The sum of all the interior angles of a polygon remains the same according to the number of sides regardless of the shape of the polygon.

The sum of interior angles of a polygon is-

(n – 2) × 180°

Where n = number of sides of the polygon

Example

PolygonNumber of SidesSum of Interior Angles
Triangle3(3 – 2) × 180° = 180°
Quadrilateral4(4 – 2) × 180° = 360°
n-gonn(n – 2) × 180°
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