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Irregular Polygons: Definition, Examples and Properties

Irregular Polygons are polygons that don’t have all their sides equal. All the angles are not of equal measure in irregular polygons. Some examples of irregular polygons include the right triangle, isosceles triangle, scalene triangle, rectangle and many more.

In this article, we will explore irregular polygons, properties of irregular polygons, types of irregular polygons and irregular polygon formulas. We will also discuss the difference between regular and irregular polygons and solve some examples related to irregular polygons. Let’s start our learning on the topic “Irregular Polygons “.

Irregular-Polygons

Table of Content

Irregular Polygons Definition

A polygon is said to be an irregular polygon when all the sides and angles of the polygon are unequal. In other words, the polygon with all its sides and angles of different measures is called an irregular polygon. All the polygons with unequal sides and angles come under irregular polygons. Some irregular polygon examples are right triangle, isosceles triangle, scalene triangle, rectangle, irregular pentagon, irregular hexagon etc.

Properties of Irregular Polygons

Some of the properties of irregular polygons are:

  • The sides of the irregular polygons are unequal.
  • The angles of the irregular polygons are unequal.
  • Some examples of irregular polygons include rectangles, parallelograms, trapezium, right triangles, obtuse triangles and many other polygons whose sides and angles are not equal.

Examples of Irregular Polygons

There are various different examples of irregular polygons including scalene triangles, isosceles triangles, right triangles, rectangles, irregular pentagons, irregular hexahexagon many more.

Scalene Triangle

Triangle in which all the three sides are different is called as scalene triangle.

Some Formulas of Scalene Triangle

Below are some formulas related to scalene triangle.

Area = √[s (s-a) (s-b) (s-c)]

where,

  • a, b and c are sides of scalene triangle
  • s = (a + b + c) /2
  • Perimeter of Scalene Triangle = Sum of All Three Sides.

Isosceles Triangle

Triangle in which two sides are equal is called as isosceles triangle.

DerivationofAreaofIsoscelestriangle

Some Formulas of Isosceles Triangle

Below are some formulas related to isosceles triangle.

Right Triangle

Triangle with one of its angles as right angle is called right triangle.

Right Angled Triangle Diagram

Some Formulas of Right Triangle

Below are some formulas related to right triangle.

  • Area of Right triangle = (1/2) × base × height
  • Perimeter of Right triangle = Base + Perpendicular + Hypotenuse
  • Pythagoras theorem: (Hypotenuse)2 = (Base)2 + (Perpendicular)2

Rectangle

Quadrilateral whose all angles and opposite sides are equal is called as rectangle.

The four sides of rectangle include two length and two breadths. The measure of length and breadth can be equal and unequal.

Perimeter-of-Rectangle

Some Formulas of Rectangle

Below are some formulas related to rectangle.

Irregular Pentagon

Pentagon whose sides are not equal is called as the irregular pentagon.

Pentagon

Irregular Hexagon

Hexagon whose sides are not equal is called as irregular hexagon.

hex

Difference Between Irregular and Regular Polygons

Below table gives the difference between the irregular and regular polygons.

Characteristics

Regular Polygons

Irregular Polygons

Definition

The polygon with equal sides and angles is called regular polygons.

The polygon with unequal sides and angles is called irregular polygon.

Examples

Some examples of regular polygon include square, equilateral triangle etc.

Some examples of irregular polygon include rectangle, scalene triangle etc.

Measure of Sides

All sides of the polygon are equal.

All the sides of the polygon are unequal.

Measure of Angles

All angles of the polygon are equal.

All angles of the polygon are not equal.

Irregular Polygons Formulas

Different formulas of the irregular polygon like area of irregular polygon, perimeter of irregular polygon, sum of interior angle of irregular polygons, sum of exterior angles of irregular polygons are given below.

Area of Irregular Polygons

Area of irregular polygons can be determined by dividing the irregular polygon in some parts that gives regular polygons. After dividing the irregular polygons in regular parts, we find the area of these regular parts. After finding the areas we add all the areas to determine the area of irregular polygon.

Perimeter of Irregular Polygons

Perimeter of irregular polygons is obtained by adding all the lengths of all the sides of the irregular polygon.

Perimeter of Irregular Polygon = Sum of all Sides of Irregular Polygon

Sum of Interior Angles of Irregular Polygons

Sum of interior angles of irregular polygon is obtained by subtracting 2 from number of sides of irregular polygon and then multiplying the resultant by 180°. The formula for the sum of interior angles of the irregular polygon is same as the formula for the sum of interior angles of regular polygon.

Sum of interior angles of irregular polygon = (n – 2) × 180°

Sum of Exterior Angles in Irregular Polygons

Sum of exterior angles in irregular polygon is equal to 360°. It is same as the sum of exterior angles of the regular polygons.

Sum of exterior angles in irregular polygon = 360°

Read More,

Examples on Irregular Polygons

Example 1: Find the perimeter of the rectangle with length 12 cm and breadth 5 cm.

Solution:

Area of Rectangle = length × breadth

Area of Rectangle = 12 × 5

Area of Rectangle = 60 cm2

Example 2: Find the sum of interior angles of irregular polygon with 15 sides.

Solution:

Sum of interior angles of irregular polygon = (n – 2) × 180°

Sum of interior angles of irregular polygon with 15 sides = (15 – 2) × 180°

Sum of interior angles of irregular polygon with 15 sides = 13 × 180°

Sum of interior angles of irregular polygon with 15 sides = 2340°

Example 3: Find the area of the right- triangle with base 12 cm and height 5 cm.

Solution:

Area of Right Triangle = (1/2) × base × height

Area of Right Triangle = (1/2) × 12 × 5

Area of Right Triangle = 30 cm2

Practice Questions on Irregular Polygons

Q1: Find the area of the scalene triangle with sides 10cm, 20 cm and 17 cm.

Q2: Find the sum of interior angles of irregular polygon with 10-sides.

Q3: Find the perimeter of the irregular hexagon with sides 10 units, 2 units, 13 units, 9 units, 15 units and 5 units.

Q4: Find the area of rectangle with length and breadth 9 cm and 4 cm respectively.

FAQs on Irregular Polygons

What is Irregular Polygon?

Polygons with sides and angles are unequal are called as irregular polygons. It is opposite of regular polygon.

What is the Difference Between Regular and Irregular Polygons?

Regular polygons are the polygons with equal sides whereas the polygons with unequal sides are called irregular polygons.

What is a 5-Sided Irregular Polygon Called?

5-sided irregular polygon is called as irregular pentagon.

What is an Irregular 4-Sided Shape?

Irregular 4-sided shape is a quadrilateral with unequal sides like rectangle, parallelogram, trapezium etc.


 


Reffered: https://www.geeksforgeeks.org

Mathematics

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