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Polygon in Maths is a two-dimensional shape made up of straight lines that form a closed polygonal chain. The word “polygon” comes from the words “poly” and “gon”, which mean “many” and “sides”. Polygons can be simple or self-intersecting. A simple polygon does not intersect itself, except at the shared endpoints of consecutive segments. A polygonal chain that crosses over itself creates a self-intersecting polygon. Polygons can also be classified as concave or convex. In this article, we have mentioned in detail about Polygons and their types, formulas, and examples.
Table of Content What are Polygons?The term ‘Polygon’ originates from the Greek word “polugonos”, where ‘poly’ signifies ‘many,’ and ‘gon’ denotes ‘angle.’ Generally, a polygon is a closed figure formed by straight lines, with its interior angles created by these lines. To constitute a closed shape, a minimum of three-line segments is necessary. It is commonly known as a Triangle or a 3-gon. The general term for an n-sided Polygon is an n-gon. Polygon DefinitionPolygons are flat, two-dimensional figures composed of straight sides that form a fully enclosed shape. In geometry, the polygon is a plane figure made up of line segments connected to form a closed polygonal chain. They consist of straight sides, not curves, and can have any varying number of sides. Some polygons of different kinds are: open, boundary only, closed and self-intersecting.
A Polygon lacks curved sides, and its edges are the straight segments defining its boundary. The meeting points of these edges are termed vertices or corners. Polygon ExamplesIn terms of mathematics triangles, hexagons, pentagons, and quadrilaterals are examples of Polygons. Real-life examples of Polygon are rectangular-shaped screen on your laptop, television, mobile phone; rectangular football pitch or playground, Bermuda Triangle and Egypt’s Pyramids of triangular shape.
Parts of a PolygonA Polygon comprises three fundamental components:
Polygon Chart based on Number of SidesNomenclature of Polygon defined on the basis of number of sides they possess. It is designated as n-gons, where ‘n’ signifies the number of sides. Polygons are generally identified by the quantity of their edges. For example, a polygon with five sides is termed a 5-gon, while one with ten sides is referred to as a 10-gon.
Properties of PolygonsThe properties of Polygons identify them easily. The following properties contribute to know the Polygons easily:
Polygon ShapesA Polygon is a flat, two-dimensional shape characterized by straight sides connected to form a closed figure. Examples of Polygon shapes include: Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Types of PolygonsDepending on the sides and angles, the Polygons can be classified into different types on different basis such as:
Polygons on the Basis of SidesPolygons can be categorized based on the characteristics of their sides into two primary types:
Regular PolygonA Regular Polygon is distinguished by having all sides of equal length and all interior angles with equal measurements. It can be both equilateral and equiangular. Examples of regular polygons include the triangle, quadrilateral, pentagon, and hexagon. -300.png) Regular Polygon Irregular PolygonAn Irregular Polygon has unequal length sides and angles of varying measures. Any polygon that does not conform to the criteria of a regular polygon is classified as irregular. Common examples of irregular polygon are the scalene triangle, quadrilaterals like rectangle, trapezoid, or kite, as well as irregular pentagon and hexagon structures. -300.png) Irregular Polygon Polygons On Basis of AnglesPolygons can be classified based on the nature of their angles into two main categories: Convex PolygonA convex polygon has no interior angle that measures more than 180°. Convex polygons can have three or more sides. In convex polygons, all diagonals lie inside the closed figure. Common examples of convex polygons are triangles, all convex quadrilaterals, as well as regular pentagons and hexagons Concave PolygonA concave polygon has at least one interior angle that is a reflex angle and points inwards. Concave polygons have a minimum of four sides. This type of polygon features at least one interior angle measuring more than 180°. In concave polygons, some diagonals extend outside the enclosed figure. Examples of concave polygons include a dart or an arrowhead in quadrilaterals, as well as certain irregular pentagons and hexagons. Difference between Concave vs Convex PolygonsLet’s see the difference between Convex and Concave Polygon in the table below:
Polygons On Basis of BoundariesPolygons can be categorized based on the nature of their boundaries into two primary types:
Simple PolygonA Simple Polygon is characterized by a singular, non-intersecting boundary. In other words, it does not cross itself, and it consists of one boundary.  Simple Polygons Complex PolygonOn the other hand, a Complex Polygon is defined by intersect itself. It consists of more than one boundary within its structure. In Complex polygons boundary intersects, creating multiple distinct regions within the polygon. -300.png) Complex Polygon Read More about Types of Polygons. Polygon FormulasThere are several formulas related to polygons in geometry. Some of the most commonly used ones include:
All the formulas related to different polygons are discussed below: Area of PolygonsArea of a Polygon represents the total space it occupies in a two-dimensional plane, is determined by specific formulas based on the number of sides and the polygon’s classification. The area formulas are as follows:
Perimeter of PolygonsThe Perimeter of a two-dimensional shape represents the total length of its outer boundary. For Polygons, the Perimeter is calculated as follows:
Diagonal of Polygon FormulaA Diagonal of a Polygon is a line segment formed by connecting two vertices that are not adjacent.
Where ‘n’ represents the number of sides the Polygon possesses. Read More about Diagonal of Polygon Formula. Angles in PolygonsIn geometry, angles in polygons refer to the angles formed by the sides of a polygon, both in the interior and exterior of the polygon. Thus, there can be both angles in polygon i.e.,
Let’s discuss the formula for these angles in detail as follows: Interior Angle Formula of PolygonsThe Interior Angles of a Polygon are those formed between its adjacent sides and are equal in the case of a regular polygon. The count of interior angles corresponds to the number of sides in the polygon. The sum of the interior angles ‘S’ in a polygon with ‘n’ sides is calculated as
Exterior Angle Formula of PolygonsEach Exterior Angle of a Regular Polygon is formed by extending one of its sides (either clockwise or anticlockwise) and measuring the angle between this extension and the adjacent side. In a regular polygon, all exterior angles are equal
Therefore,
Sum of the interior and corresponding exterior angles at any vertex in a polygon is always 180 degrees, expressing a supplementary relationship:
Conclusion
Also, Read Solved Examples on Polygon in MathsExample 1: Consider a quadrilateral with four sides. Find the sum of all its interior angles of quadrilateral. Solution:
Example 2: Consider a Regular Polygon with a given exterior and interior angle ratio of 7:3. Determine the type of polygon. Solution:
Example 3: Each Exterior Angle of a Polygon measures 90 degrees, determine the type of Polygon? Solution:
Example 4: The sides are 10m, 10m, 8m, 8m, 5m, 5m, 9m, 9m. How many meters of rope will be needed for the Perimeter? Solution:
Practice Questions on Polygons in GeometryFollowing are some practice questions based on the formula of polygons: Q1. Given one angle of a pentagon is 140°, determine the size of the largest angle if the remaining angles are in the ratio 1:2:3:4. Q2. If the sum of the interior angles of a polygon is 160°, find the number of sides in the Polygon. Q3. The number of sides in two regular polygons are in the ratio 2:3, and the ratio of their interior angles is 4:5. Find the respective numbers of sides of these Polygons. Q4. Determine the total sum of angles in a heptagon. Q5. Calculate the sum of exterior angles in a pentagon. Q6. How many sides does a hexagon have?
Q7. Which of the following is not a regular polygon?
FAQs on Polygons in MathsWhat is a Polygon in Maths?
Which is the Smallest Polygon?
What is 20-gon?
What is the Total Sum of External Angles of Polygon?
Can a Circle be Classified as a Polygon?
What is the Sum of Interior Angle of a Polygon?
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| Class 7 |
Type: | Geek |
Category: | Coding |
Sub Category: | Tutorial |
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