In our regular life we can see many types of figures/ shapes/structures. A simple closed figure which is formed by three or more lines or more than three lines is called a polygon.
If a polygon has n-sides then it is said to be N-gon. i.e. for example see the below polygon it has 4 sides and it is said to be 4-gon.
Diagonal of a polygon:- A line segment which is joining any two non-consecutive vertices of a polygon is called its diagonal. Observe the Figure-1 Here A and C joins with a line segment AC like wise BD also so here AC,BD are called Diagonal of the polygon.
Here Vertices are A,B,C and D.
To find the No.of diagonal of a n-sided polygon we can use the below formula
[n(n-3)]/2 here n is no of sides of the polygon.
Consider the above figure we have n is 4 here and substitute the n value as 4 here then we get 2.
Polygons are basically Two types those are:
1. Convex polygon
Convex polygon: In this type of polygon each angle is measured less than 180 degrees means two right angles such a polygon is called convex polygon.
Concave polygon: In this type of polygon if an angle is measured 180 degrees means two right angles such a polygon is called concave polygon.
Angles of a polygon: Basically polygons having two types of angles those are Exterior and interior angles.
Interior angle Exterior angle:
An angle inside the polygon is called the interior angle (Green color i the picture) and an angle outside of the polygon is called exterior angle(Red color in the Picture).
Sum of the outside angle of polygon is 360 degrees.
Each exterior angle is measured by using 360/n here n is side of the polygon.
Sum of interior angle of a polygon is (n-2)*180 degrees. here n is side of the polygon.
Each interior angle is measured by using [(n-2)*180]/n , here n is side of the polygon.
- For example a polygon has 5 sides then find the each exterior and interior angle and sum of the interior and exterior angle.
- Sum of exterior angle is =360 degrees.
- Sum of interior angle is (n-2)*180 here n is 5
- Each exterior angle is 360/n n is 5 here so 360/5=72 degrees.
- Each interior angle is [(n-2)*180]/n here n is 5 so by using formula we get 108 degrees.
- Apart from this polygons are divide into two those are Equilateral and Equiangular.
- A polygon in which all sides are equal then is called equilateral polygon . example is Rhombus.
- A polygon in which all angles are equal then is called equiangularl polygon . example is rectangle.