What is a Regular Polygon?
A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides or edges of a polygon are made of straight line segments connected end to end to form a closed shape. The point where two line segments meet is called vertex or corners, and subsequently, an angle is formed. If a polygon contains congruent sides, then that is called a regular polygon. The below figure shows several types of polygons.
All the shapes in the above figure are the regular polygons with different number of sides.
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What are Regular Polygons?
If all the sides and interior angles of the polygons are equal, they are known as regular polygons. The examples of regular polygons are square, rhombus, equilateral triangle, etc.
In regular polygons, not only the sides are congruent but angles are too. That means, they are equiangular.
Properties of Regular polygons
Some of the properties of regular polygons are listed below.
- All the sides of a regular polygon are equal
- All the interior angles are equal
- The perimeter of a regular polygon with n sides is equal to the n times of a side measure.
- The sum of all the interior angles of a simple n-gon or regular polygon = (n − 2) × 180°
- The number of diagonals in a polygon with n sides = n(n – 3)/2
- The number of triangles formed by joining the diagonals from one corner of a polygon = n – 2
- The measure of each interior angle of n-sided regular polygon = [(n – 2) × 180°]/n
- The measure of each exterior angle of an n-sided regular polygon = 360°/n
Some of the regular polygons along with their names are given below:
Equilateral Triangle:
Equilateral triangle is the regular polygon with the least number of possible sides.
The number of sides = 3
The sum of all interior angles = 180°
The measure of each interior angle = 60°
Square:
Square is a quadrilateral with four equal sides and it is called a 4-sided regular polygon.
The number of sides = 4
The sum of all interior angles = 360°
The measure of each interior angle = 90°
Regular Pentagon
A Pentagon or 5-gon with equal sides is called a regular pentagon.
The number of sides = 5
The sum of all interior angles = 540°
The measure of each interior angle = 108°
Regular Hexagon:
Hexagon is a 6-sided polygon and it is called a regular hexagon when all of its sides are equal.
The number of sides = 6
The sum of all interior angles = 720°
The measure of each interior angle = 120°
Similarly, we have regular polygons for heptagon (7-sided polygon), octagon (8-sided polygon), and so on.
What is a Regular Polygon of 7 sides called?
A regular polygon of 7 sides called a regular heptagon. The sum of all interior angles of this polygon is equal to 900 degrees, whereas the measure of each interior angle is approximately equal to 128.57 degrees. However, the below figure shows the difference between a regular and irregular polygon of 7 sides.
What is a Regular Polygon with 4 sides?
A regular polygon with 4 sides is called a square. It is a quadrilateral with four equal sides and right angles at the vertices.
Area of Regular Polygon
In this section, the area of regular polygon formula is given so that we can find the area of a given regular polygon using this formula.
The formula for the area of a regular polygon is given as,
Where,
l is the side length
n is the number of sides
Also, get the area of regular polygon calculator here.
Visit byjus.com to get more knowledge about polygons and their types, properties. Also, download BYJU’S – The Learning App for interactive videos on maths concepts.
Frequently Asked Questions on Regular Polygon
What is meant by a regular polygon?
A polygon possessing equal sides and equal angles is called a regular polygon. Square is an example of a regular polygon with 4 equal sides and equal angles.
What is a regular polygon? Give two examples.
A regular polygon is a polygon with congruent sides and equal angles. The examples of regular polygons include equilateral triangle, square, regular pentagon, and so on.
How do you know if a polygon is regular?
If the given polygon contains equal sides and equal angles, then we can say that the given polygon is regular; otherwise, it is irregular.
What is a 4 sided shape called?
In geometry, a 4 sided shape is called a quadrilateral. In other words, a polygon with four sides is a quadrilateral. Some of the examples of 4 sided shapes are:
Square
Rectangle
Parallelogram
Rhombus
What is an L shape called?
A right angle concave hexagon can have the shape of L.
What is the difference between a polygon and a regular polygon?
A polygon is a simple closed two-dimensional figure with at least 3 straight sides or line segments. A regular polygon is a type of polygon with equal side lengths and equal angles.
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