Definition of polygons:
Polygons are the two dimensional closed figure that is made up of three or more than three line segments.
Types of polygons:
regular polygons
irregular polygons
convex polygons
concave polygons
Crossed polygons.
Basic Criteria that Helps in Identifying Polygons:
Identification of regular polygon:
In this polygons
All the sides of the polygons are equal in length
All the angles of the polygons are equal in degrees.
Regular polygons are convex
Identification of irregular polygon
In this polygons
No the sides of the polygons are equal in length
All the angles of the polygons are different in degrees.
Irregular polygons are convex or concave.
Identification of convex polygon:
Here
The internal angle of the polygon is equal to 180 or less than 180 degrees
Identification of concave polygon:
Here
The one or more internal angle of the polygon is greater than 180 degrees
Formula to identify the regular polygons:
Internal angle of regular polygon= `(((M-2)*180)/M)` degrees
External angle of the regular polygon = 180- internal angle of regular polygon.
Number of diagonals in a polygon= `(M (M-3))/2`
Here M is the number of sides of the regular polygon.
Area of regular Polygon = 1/2× M × Radius2 × sin (2 × p/n)
Area of regular Polygon = 1/4 × M× Side2 / tan (p/n)
I like to share this geometric probability formula with you all through my article.
Using this Formula, we can Find the Identify the Type of the Polygon.
Model problem 1:
Help to identify the polygon whose sides are equal and the number of the sides is 6 and internal angle is 120 degrees:
Solution:
Number of the sides of the polygon is 6
Internal angle is 120 degrees
All the sides are equal.
From the given condition, we can conclude the given polygon is regular hexagon.
Here the internal angle is less than 180 degrees
So it is a convex one
The polygon is regular hexagon convex polygon.
2.Help to identify the polygon whose sides are equal and the number of the sides is 8 and internal angle is 135 degrees:
Solution:
Number of the sides of the polygon is 8
Internal angle is 135 degrees
All the sides are equal.
From the given condition, we can conclude the given polygon is regular octagon
Here the internal angle is less than 180 degrees
So it is a convex one
The polygon is regular octagon convex polygon.
Polygons are the two dimensional closed figure that is made up of three or more than three line segments.
Types of polygons:
regular polygons
irregular polygons
convex polygons
concave polygons
Crossed polygons.
Basic Criteria that Helps in Identifying Polygons:
Identification of regular polygon:
In this polygons
All the sides of the polygons are equal in length
All the angles of the polygons are equal in degrees.
Regular polygons are convex
Identification of irregular polygon
In this polygons
No the sides of the polygons are equal in length
All the angles of the polygons are different in degrees.
Irregular polygons are convex or concave.
Identification of convex polygon:
Here
The internal angle of the polygon is equal to 180 or less than 180 degrees
Identification of concave polygon:
Here
The one or more internal angle of the polygon is greater than 180 degrees
Formula to identify the regular polygons:
Internal angle of regular polygon= `(((M-2)*180)/M)` degrees
External angle of the regular polygon = 180- internal angle of regular polygon.
Number of diagonals in a polygon= `(M (M-3))/2`
Here M is the number of sides of the regular polygon.
Area of regular Polygon = 1/2× M × Radius2 × sin (2 × p/n)
Area of regular Polygon = 1/4 × M× Side2 / tan (p/n)
I like to share this geometric probability formula with you all through my article.
Using this Formula, we can Find the Identify the Type of the Polygon.
Model problem 1:
Help to identify the polygon whose sides are equal and the number of the sides is 6 and internal angle is 120 degrees:
Solution:
Number of the sides of the polygon is 6
Internal angle is 120 degrees
All the sides are equal.
From the given condition, we can conclude the given polygon is regular hexagon.
Here the internal angle is less than 180 degrees
So it is a convex one
The polygon is regular hexagon convex polygon.
2.Help to identify the polygon whose sides are equal and the number of the sides is 8 and internal angle is 135 degrees:
Solution:
Number of the sides of the polygon is 8
Internal angle is 135 degrees
All the sides are equal.
From the given condition, we can conclude the given polygon is regular octagon
Here the internal angle is less than 180 degrees
So it is a convex one
The polygon is regular octagon convex polygon.
