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 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.
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.
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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.
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.
Irregular Hexagon
Hexagon whose sides are not equal is called as irregular hexagon.
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. |
|---|
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°
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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.
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