In Geometry, a polygon is a closed two-dimensional figure, which is made up of straight lines. Generally, from the name of the polygon, we can easily identify the number of sides of the shape. For example, a triangle is a polygon which has three sides. Here, let us discuss the polygon definition, types of a polygon, its formula, properties with an example.
Polygon Definition in Maths
In Mathematics, a polygon is a closed two-dimensional shape having straight line segments. It is not a three-dimensional shape. A polygon does not have any curved surface. A polygon should have at least three sides. Each side of the line segment must intersect with another line segment only at its endpoint. Based on the number of sides of a polygon, we can easily identify the polygon shape. The list of polygon shapes with the number of sides is given below.
No. of Sides | Polygon Shape |
3 | Triangle |
4 | Quadrilateral |
5 | Pentagon |
6 | Hexagon |
7 | Heptagon |
8 | Octagon |
9 | Nonagon |
10 | Decagon |
Types of Polygon
Based on the angle measure and the sides of a polygon, the polygon is classified into:
- Regular Polygon – All the interior angles and the sides are equal
- Irregular Polygon – All the interior angles and the sides are of different measure
- Convex polygon – All the interior angles of a polygon are strictly less than 180 degrees
- Concave Polygon – One or more interior angles of a polygon are more than 180 degrees
Polygon Formula
The important polygon formulas are:
- The sum of interior angles of a polygon with “n” sides =180°(n-2)
- Number of diagonals of a “n-sided” polygon = [n(n-3)]/2
- The measure of interior angles of a regular n-sided polygon = [(n-2)180°]/n
- The measure of exterior angles of a regular n-sided polygon = 360°/n
Polygon Properties
The important properties of the polygon are
- The sum of interior angles of all the quadrangles is equal to 360 degrees.
- If at least one of the interior angles is greater than 180 degrees, then it is called concave
- If a polygon does not cross over itself, and has only one boundary, it is called a simple polygon. Otherwise, it is a complex polygon
Polygon Example
Question:
Find the sum of the interior angle of a pentagon
Solution:
We know that a pentagon has five sides.
The formula to find the sum of interior angles is given by:
Interior angle sum = 180°(n-2)
= 180°(5-2)
= 180° (3)
= 540°
Hence, the sum of the interior angles of a pentagon is 540°
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FAQs
Types of Polygon
Regular Polygon – All the interior angles and the sides are equal. Irregular Polygon – All the interior angles and the sides are of different measure. Convex polygon – All the interior angles of a polygon are strictly less than 180 degrees.
What is the formula of types of polygon? ›
Area and Perimeter Formulas
| Name of polygon | Area | Perimeter |
|---|
| Parallelogram | Base x Height | 2(Sum of pair of adjacent sides) |
| Trapezoid | Area = 1/2 (sum of parallel side)height | Sum of all sides |
| Rhombus | ½ (Product of diagonals) | 4 x side |
| Pentagon | 1 4 5 ( 5 + 2 5 ) s i d e 2 | Sum of all five sides |
4 more rowsIf the number of sides of a polygon is given, the area of the polygon can be calculated with the help of the formula, Area = [(L2 n)/4 tan(180/n)]; where L is the length of its side and 'n' is the number of sides of the polygon.
What is the definition of polygon in math and example? ›
A polygon is any 2-dimensional shape formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons. The name tells you how many sides the shape has. For example, a triangle has three sides, and a quadrilateral has four sides.
What are the 7 polygons? ›
They are:
- Regular Polygons.
- Irregular Polygons.
- Concave Polygons.
- Convex Polygons.
- Trigons.
- Quadrilateral Polygons.
- Pentagon Polygons.
- Hexagon Polygons.
A shape is a polygon if it has the following characteristics:
- The shape must be a closed shape, that is, it must end and begin at the same point.
- The shape should be made of line segments or straight lines.
- The shape must be a two-dimensional figure, that is, it must have only two dimensions length and width.
They can be classified as convex and not convex; as regular or irregular. Polygons are also classified by how many sides they have. The following table lists the different types of polygons, with the name ande major characteristics of the polygons.
What is the formula for regular and irregular polygon? ›
The interior angles in an irregular polygon are not equal to each other. Therefore, to find the sum of the interior angles of an irregular polygon, we use the formula the same formula as used for regular polygons. The formula is: Sum of interior angles = (n − 2) × 180° where 'n' = the number of sides of a polygon.
What is the formula for angles and polygons? ›
The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.
How many sides of a polygon formula? ›
To calculate the number of sides of the polygon, divide 360 by the amount of the exterior angle. For example, if the exterior angle is 60 degrees, then dividing 360 by 60 equals 6, which is the number of sides the polygon has.
If it is a regular polygon, the formula that is used is, Perimeter = number of sides × length of one side. If it is an irregular polygon, then the sides can be added to find the perimeter using the formula, Perimeter = Sum of the sides.
What are the properties of polygons? ›
A regular polygon has equal length sides with equal angles between each side. Any other polygon is an irregular polygon, which by definition has unequal length sides and unequal angles between sides. Circles and shapes that include curves are not polygons - a polygon, by definition, is made up of straight lines.
What is the best example of polygon? ›
Triangles, hexagons, pentagons, and quadrilaterals are all examples of polygons. The name gives an indication of how many sides the shape has. For example, a triangle consists of three sides while a quadrilateral consists of four sides.
What are 12 polygons? ›
A dodecagon is a 12-sided polygon. Several special types of dodecagons are illustrated above. In particular, a dodecagon with vertices equally spaced around a circle and with all sides the same length is a regular polygon known as a regular dodecagon.
What shape has 100000000 sides? ›
A megagon or 1 000 000-gon is a polygon with 1 million sides (mega-, from the Greek μέγας megas, meaning "great"). Even if drawn at the size of the Earth, a regular megagon would be very difficult to distinguish from a circle.
What is the name of the 20 polygon? ›
In geometry, an icosagon or 20-gon is a twenty-sided polygon. The sum of any icosagon's interior angles is 3240 degrees.
What are the 4 sided polygons? ›
There are 6 different 4 sided polygons, or quadrilaterals that receive their own names. They are rectangles, squares, parallelograms, rhombuses, kites and trapezoids.
