# Polygon Shape

Sizes and shapes are the backbones of geometry. One of the most encountered shapes in geometry is polygons.

In this mini-lesson, we will explore the world of the polygon by finding the answers to the questions like what is a polygon, polygon shapes, polygon angles, sides of a polygon, and types of a polygon. Let us explore the chapter 'Polygon-Shapes' in detail.

## Lesson Plan

 1 What Is A Polygon? 2 Important Notes on Polygon Shapes 3 Solved Examples On Polygon Shapes 4 Interactive Questions On Polygon Shapes 5 Challenging Questions On Polygon Shapes

## What Is A Polygon?

In geometry, a polygon is a closed two-dimensional figure with three or more straight lines.

The Greek word ‘Polygon’ consists of Poly meaning ‘many’ and gon meaning ‘angle.’

We see many different polygons around us.

For example, Have you ever seen a honeycomb? Can you guess ideally, how many sides a honeycomb could have?

A honeycomb is hexagonal in shape. You can very well relate the shape of a 6 sided polygon with a honeycomb.

## Polygon Shape: Images

In geometry, we have different kinds of polygons with respect to the sides.

Have a look at the shapes below.

These are some of the examples of polygon shapes

Each polygon is different in structure, they are categorized based on the number of sides and their properties.

### Polygon Chart

These are some of the familiar polygon shapes.

## Polygon Angles

Look at the pentagon shape. It has two types of angles.

• Interior angles - Angles measured between two sides of a polygon
• Exterior angles - Angles formed between any side to a line extended in its adjacent side.

The interior angles are formed inside and the exterior angles are formed outside the pentagon.

The following polygon formula can be used to find polygon angles.

 $$\text{Exterior Angle} = \frac{360^{\circ}}{n}$$
 $$\text{Interior angle} =\frac{180^{\circ}(n-2)}{n}$$

Where $$n$$ is number of sides.

Try your hands on this interesting simulation to know about angles of different shapes of a polygon.

Important Notes
1. Polygons are 2-D figures with more than $$3$$ sides.
2. angles of a polygon can be measure by using the following formulas:
$$\text{Exterior Angle} = \frac{360^{\circ}}{n}$$
$$\text{Interior angle} =\frac{180^{\circ}(n-2)}{n}$$
Here $$n$$ refers to the number of side.

## How Many Sides Are There in a Polygon?

A polygon consists of three or more sides.

For instance, a triangle has $$3$$ sides, a quadrilateral has $$4$$ sides, a pentagon has $$5$$ sides, and so on.

In the next section of this chapter, we will discuss different polygons shapes with different sides in detail.

## What Are The Types of Polygons?

The types of polygons are categorized into three major forms.

### Regular or Irregular Polygon

A polygon is said to be regular if it has equal length on all of its sides and with equal angles at each vertex.

A polygon is said to be irregular if its sides are not equal and angles differ from each other.

 Regular Polygons Irregular Polygons

### Concave or Convex Polygon

A polygon in which at least one of the interior angles is greater than $$180^\circ$$ is called a concave polygon.

A polygon whose every interior angle is less than $$180^\circ$$ is called a convex polygon

 Concave Polygons Interior angle is greater than $$180^\circ$$ Convex Polygons Interior angle is less than $$180^\circ$$

### Simple or Complex Polygon

A simple polygon is a polygon that does not intersect itself.

A polygon that intersects itself and has more than one boundary is called a complex polygon.

 Simple Polygons Complex Polygons

## 3-20 Sides of A Polygon

Let us look at a few different types of polygons with their sides

Sides

Shape and Name of A Polygon

3
Trigon
4
Tetragon
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
10
Decagon
11

Hendecagon

12
Dodecagon
13

Tridecagon

14
15
16
17
18
19
20
Icosagon

## Solved Examples

 Example 1

Help Ruth figure out the polygon shape in the hanger.

Solution

The hanger looks like a trigon or three-sided polygon.

 $$\therefore$$ The hanger resembles a trigon.
 Example 2

Anna needs help in picking the only hexagon polygons.

Solution

A hexagon has $$6$$ sides.

So Anna should pick the polygon with only $$6$$ sides.

The $$6$$-sided polygons are

 $$\therefore$$ Anna picked all the hexagon polygons.
 Example 3

James is very eager to find the interior angle of a regular hexagonal-shaped signboard "STOP".

Help James in finding out its interior angle.

Solution

The signboard is a regular polygon.

The number of sides in a signboard is $$8$$

The signboard resembles an octagon shape.

The interior angle of a regular polygon is,

\begin{align}\text{Interior angle}&=\frac{180^{\circ}(n-2)}{n}\\\ &=\frac{180^{\circ}(8-2)}{8}\\\ &=135^{\circ}\end{align}

 $$\therefore$$ Interior angle of a signboard is $$135^{\circ}$$.

## Interactive Questions

Here are a few activities for you to practice.

Select/Type your answer and click the "Check Answer" button to see the result.

Challenging Questions
1. Is a circle a polygon?
2. Find the sum of the interior angles of the following polygons:
a) regular tridecagon

## Let's Summarize

The mini-lesson targeted the fascinating concept of a polygon shape. The math journey around polygon shape starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. Here lies the magic with Cuemath.

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.

## 1. What is the difference between a regular and irregular polygon?

A polygon whose length is equal on all sides with equal angles at each vertex is called a regular polygon.

An irregular polygon is a polygon whose sides are not equal and angles differ from each other.

## 2. What are concave and convex polygons?

The polygons in which at least one of the interior angles is greater than 180º are called concave polygons.

The polygons whose every interior angle is less than 180º are called convex polygons.

## 3. What are simple and complex polygons?

A simple polygon is a polygon that does not intersect itself.

The polygons which intersect themselves and have more than one boundary are called complex polygons.

## 4. How do you calculate the sum of the interior angles of a polygon?

If a polygon is a regular polygon, then the $$\text{Interior angle} = \frac{180^{\circ}(n-2)}{n}$$.

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