Class 8 - Types Of Polygon

A polygon is a closed two dimensional shape made with straight sides. It has at least three sides, three angles, and three vertices. The word “poly” means many, and “gon” means angle. For example, a triangle is a polygon because it has three sides, three angles, and three vertices. Polygons can be classified in different ways, such as by the number of sides, the number of angles, and whether they are regular or irregular.

Table of Content

• What is a Polygon?
• Why Are Polygons Important?
• What are the Different Types of Polygons?
• Types of Polygons Based on Shape
• Types of Polygons Based on the Number of Their Sides
• Types of Polygons Based on Their Angles
• Types of Polygons With Sides 3 to 20
• Solved Examples on Types of Polygons

What is a Polygon?

A polygon is a closed shape made up of straight lines. These straight lines connect to form corners or angles. The word "polygon" comes from two Greek words: "poly" which means many, and "gon" which means angles or corners.

Think of a polygon as a drawing that starts at one point, goes around, and comes back to where it started. All the sides of a polygon must be straight lines. Curves are not allowed in polygons.

Why Are Polygons Important?

Polygons are important in many areas of life. Architects use polygons when designing buildings. Engineers use them in machines and bridges. Artists use polygons in their work. Nature creates polygons in honeycomb, flowers, and crystals.

Understanding polygons helps you understand the world around you. When you look at buildings, roads, and nature, you will see polygons everywhere. Learning about them makes you notice the patterns and shapes in your environment.

What are the Different Types of Polygons?

A polygon is a closed shape made with straight sides. It can have any number of sides and angles. The sides of a polygon are called edges, the corners where two edges meet are called vertices, and a line joining two opposite vertices is called a diagonal. Polygons can be classified in different ways, such as by the number of sides, the shape of the angles, the length of sides and angles, and the type of boundary. Let us now look at the types of polygons.

• Number of sides
• Angles (Concave or Convex Polygons)
• Measurement of sides and angles (Regular or Irregular Polygons)

Types of Polygons Based on the Number of Their Sides

A polygon has at least 3 sides and 3 angles. The table below shows 10 common polygons and their names based on the number of sides. When a polygon has more than 20 sides, it is usually called an n-gon. There is no special name for each larger polygon, so it is simply described as a polygon with n sides.

There are polygons that have more than 15 sides also. Polygons that have more than 20 sides are called n-gons.

Types of Polygons Based on Shape

polygons can be differentiated on the basis of the measurement of sides and angles. They are classified as:

Regular Polygons

A regular polygon has all sides of equal length and all angles of equal size. Think of a square. All four sides are the same length, and all four angles are the same size. Regular polygons look perfect and balanced.

Regular triangles (also called equilateral triangles) have three equal sides and three equal angles. A regular hexagon has six equal sides and six equal angles.

Irregular Polygons

An irregular polygon has sides that are not all the same length. The angles are also not all the same size. A rectangle is an irregular quadrilateral because the sides have different lengths (unless it is a square).

Most polygons you find in real life are irregular. They are still important and useful, even though they are not perfectly balanced.

Types of Polygons Based on Their Angles

Polygons can also be sorted by the types of angles they have. This is another important way to understand different polygons.

Convex Polygons

A convex polygon is one where all the angles point outward. If you draw a straight line around the outside of a convex polygon, that line will touch every side. None of the sides bend inward. Think of a square or a regular pentagon. These shapes look balanced and even.

When you look at a convex polygon, no part of it goes "inside" the shape. All the corners point outward in a friendly way. Most common polygons you see are convex.

Concave Polygons

A concave polygon has at least one angle that points inward. This makes the shape look uneven or unusual. Imagine a star shape. Stars have points that stick out and areas that go in. That is a concave polygon.

With concave polygons, if you draw a straight line around the outside, some parts will not touch the line. These shapes are trickier to work with and less common than convex polygons.

Types of Polygons With Sides 3 to 20

Here is a table showing all polygon names from 3 sides to 20 sides:

Solved Examples on Types of Polygons

1. Triangle

Question: Find the area of a triangle with base 10 cm and height 6 cm.

Solution: Area = (1/2) × base × height

= (1/2) × 10 × 6

= 30 cm²

2. Square

Question: Find the area of a square with side 8 cm.

Solution:

Area = side × side

= 8 × 8

= 64 cm²

3. Rectangle

Question: Find the area of a rectangle with length 12 cm and width 5 cm.

Solution:

Area = length × width

= 12 × 5

= 60 cm²

4. Parallelogram

Question: Find the area of a parallelogram with base 9 cm and height 4 cm.

Solution:

Area = base × height

= 9 × 4

= 36 cm²

5. Trapezium (Trapezoid)

Question: Find the area of a trapezium with parallel sides 7 cm and 11 cm, and height 5 cm.

Solution:

Area = (1/2) × (sum of parallel sides) × height

= (1/2) × (7 + 11) × 5

= (1/2) × 18 × 5

= 45 cm²

Conclusion

Polygons are fundamental shapes that form the building blocks of geometry. From simple triangles to complex twenty-sided shapes, each polygon has its own properties and uses. By understanding the different types of polygons based on their sides and angles, you gain important knowledge about mathematics and how shapes work.