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 sides||Name of Polygon||Figure|
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 –
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
|Polygon||Number of Sides||Sum of Interior Angles|
|Triangle||3||(3 – 2) × 180° = 180°|
|Quadrilateral||4||(4 – 2) × 180° = 360°|
|n-gon||n||(n – 2) × 180°|