Polygons

MATHEMATICS • Form 1 • Chapter 9: Basic Polygons

9.1 Polygons

In this topic, students learn about polygons, the relationship between the number of sides, vertices and diagonals, and how to draw, label and name polygons.

Learning Objectives

  • State the relationship between the number of sides, vertices and diagonals of polygons.
  • Determine the number of vertices and diagonals of a polygon.
  • Draw polygons according to the number of sides.
  • Label the vertices of polygons.
  • Name polygons according to their number of sides.

Know Polygons

Learn the meaning of polygons, examples of shapes and polygon names according to the number of sides.

Basic Polygons Infographic

Brief Explanation

What is a Polygon?

Poligon is a closed shape on a plane bounded by three or more straight lines.

How is a polygon named?

A polygon is named according to the number of its sides. For example, a polygon with 6 sides is called a hexagon.

Number of sides Name of polygon Brief note
3 Triangle Polygon with 3 sides
4 Quadrilateral Polygon with 4 sides
5 Pentagon Polygon with 5 sides
6 Hexagon Polygon with 6 sides
7 Heptagon Polygon with 7 sides
8 Octagon Polygon with 8 sides
9 Nonagon Polygon with 9 sides
10 Decagon Polygon with 10 sides
1
Identify the number of sides
Count the number of sides of the polygon.
2
Mark the points
Mark points equal in number to the number of sides.
3
Join the points
Join all the points with straight lines to form a closed figure.
4
Label and name
Label the vertices and name the polygon.

Interactive: Explore Polygons

Choose a polygon name to see its number of sides, vertices, diagonals and angles.

 
Click the image to show / hide the angles.
3 sides · 3 vertices

Triangle

3-sided polygon.

Number of sides
3
Number of vertices
3
Number of diagonals
0
1 Identify the number of sides of the polygon.
2 Mark points equal in number to the number of sides.
3 Join all the points with straight lines to form a closed figure.
4 Label the vertices and name the polygon.
Quick Polygon Quiz
Score: 0 / 0
 
 
 
Triangle
3 sides • 3 vertices • 0 diagonals
Quadrilateral
4 sides • 4 vertices • 2 diagonals
Pentagon
5 sides • 5 vertices • 5 diagonals
Hexagon
6 sides • 6 vertices • 9 diagonals
Heptagon
7 sides • 7 vertices • 14 diagonals
Octagon
8 sides • 8 vertices • 20 diagonals
Nonagon
9 sides • 9 vertices • 27 diagonals
Decagon
10 sides • 10 vertices • 35 diagonals
Number of diagonals = n(n − 3) ÷ 2    (n = number of sides)

Try Answering First

Read the question, answer it in your mind, then press “Check Answer”.

1

What is the meaning of polygon?

Answer: A polygon is a closed shape on a plane bounded by three or more straight lines.
2

Name the polygon that has 8 sides.

Answer: Octagon.
3

Find the number of vertices for a polygon with 10 sides.

Answer: Number of vertices = number of sides. Therefore, the number of vertices = 10.

Common Mistakes

  • ! Thinking that an open shape is a polygon. A polygon must be a closed shape.
  • ! Using curved lines as polygon sides. Polygon sides must be straight lines.
  • ! Naming polygons wrongly, for example, 6 sides is a hexagon, not a pentagon.
  • ! Not labelling vertices in alphabetical order.
  • ! Marking three or more points in a straight line when drawing a polygon.

Misconceptions

Misconception

All closed shapes are polygons.

Correct Fact

A polygon must have sides made of straight lines.

Misconception

The name of a polygon depends on the size of the shape.

Correct Fact

The name of a polygon depends on the number of sides.

Misconception

Vertex labels can be placed randomly.

Correct Fact

Vertices are usually labelled in alphabetical order.

Summary

  • A polygon is a closed shape with three or more straight lines.
  • The number of vertices of a polygon is the same as the number of its sides.
  • The name of a polygon is determined by its number of sides.
  • To draw a polygon, mark the points, join the points, label the vertices and name the polygon.
  • The number of diagonals can be found using the given steps or the formula n(n − 3) / 2.

Short Activity

Complete all parts first, then press the check answer button.

A. Objective Quiz

1 A polygon is a on a plane with sides made of straight lines.

2 A polygon that has 6 sides is called a .

B. Fill in the Blanks

3 A polygon that has 3 sides is called a .

4 A polygon that has 5 sides is called a .

C. Drag and Drop: Arrange the Steps to Draw a Polygon

Drag each step to the correct place. On a phone, tap the answer choice first, then tap the sequence box.

Answer Choices
Label the vertices and name the polygon
Identify the number of sides of the polygon
Join all the points to form a closed figure
Mark points equal in number to the number of sides
Step Sequence
1
2
3
4
 

Key Terms

Poligon Vertex Side Diagonal Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Interior angle Exterior angle

Polygons

MATHEMATICS • Form 1 • Chapter 9: Basic Polygons

9.1 Polygons

In this topic, students learn about polygons, the relationship between the number of sides, vertices and diagonals, and how to draw, label and name polygons.

Learning Objectives

  • State the relationship between the number of sides, vertices and diagonals of polygons.
  • Determine the number of vertices and diagonals of a polygon.
  • Draw polygons according to the number of sides.
  • Label the vertices of polygons.
  • Name polygons according to their number of sides.

Know Polygons

Learn the meaning of polygons, examples of shapes and polygon names according to the number of sides.

Basic Polygons Infographic

Brief Explanation

What is a Polygon?

Poligon is a closed shape on a plane bounded by three or more straight lines.

How is a polygon named?

A polygon is named according to the number of its sides. For example, a polygon with 6 sides is called a hexagon.

Number of sides Name of polygon Brief note
3 Triangle Polygon with 3 sides
4 Quadrilateral Polygon with 4 sides
5 Pentagon Polygon with 5 sides
6 Hexagon Polygon with 6 sides
7 Heptagon Polygon with 7 sides
8 Octagon Polygon with 8 sides
9 Nonagon Polygon with 9 sides
10 Decagon Polygon with 10 sides
1
Identify the number of sides
Count the number of sides of the polygon.
2
Mark the points
Mark points equal in number to the number of sides.
3
Join the points
Join all the points with straight lines to form a closed figure.
4
Label and name
Label the vertices and name the polygon.

Interactive: Explore Polygons

Choose a polygon name to see its number of sides, vertices, diagonals and angles.

 
Click the image to show / hide the angles.
3 sides · 3 vertices

Triangle

3-sided polygon.

Number of sides
3
Number of vertices
3
Number of diagonals
0
1 Identify the number of sides of the polygon.
2 Mark points equal in number to the number of sides.
3 Join all the points with straight lines to form a closed figure.
4 Label the vertices and name the polygon.
Quick Polygon Quiz
Score: 0 / 0
 
 
 
Triangle
3 sides • 3 vertices • 0 diagonals
Quadrilateral
4 sides • 4 vertices • 2 diagonals
Pentagon
5 sides • 5 vertices • 5 diagonals
Hexagon
6 sides • 6 vertices • 9 diagonals
Heptagon
7 sides • 7 vertices • 14 diagonals
Octagon
8 sides • 8 vertices • 20 diagonals
Nonagon
9 sides • 9 vertices • 27 diagonals
Decagon
10 sides • 10 vertices • 35 diagonals
Number of diagonals = n(n − 3) ÷ 2    (n = number of sides)

Try Answering First

Read the question, answer it in your mind, then press “Check Answer”.

1

What is the meaning of polygon?

Answer: A polygon is a closed shape on a plane bounded by three or more straight lines.
2

Name the polygon that has 8 sides.

Answer: Octagon.
3

Find the number of vertices for a polygon with 10 sides.

Answer: Number of vertices = number of sides. Therefore, the number of vertices = 10.

Common Mistakes

  • ! Thinking that an open shape is a polygon. A polygon must be a closed shape.
  • ! Using curved lines as polygon sides. Polygon sides must be straight lines.
  • ! Naming polygons wrongly, for example, 6 sides is a hexagon, not a pentagon.
  • ! Not labelling vertices in alphabetical order.
  • ! Marking three or more points in a straight line when drawing a polygon.

Misconceptions

Misconception

All closed shapes are polygons.

Correct Fact

A polygon must have sides made of straight lines.

Misconception

The name of a polygon depends on the size of the shape.

Correct Fact

The name of a polygon depends on the number of sides.

Misconception

Vertex labels can be placed randomly.

Correct Fact

Vertices are usually labelled in alphabetical order.

Summary

  • A polygon is a closed shape with three or more straight lines.
  • The number of vertices of a polygon is the same as the number of its sides.
  • The name of a polygon is determined by its number of sides.
  • To draw a polygon, mark the points, join the points, label the vertices and name the polygon.
  • The number of diagonals can be found using the given steps or the formula n(n − 3) / 2.

Short Activity

Complete all parts first, then press the check answer button.

A. Objective Quiz

1 A polygon is a on a plane with sides made of straight lines.

2 A polygon that has 6 sides is called a .

B. Fill in the Blanks

3 A polygon that has 3 sides is called a .

4 A polygon that has 5 sides is called a .

C. Drag and Drop: Arrange the Steps to Draw a Polygon

Drag each step to the correct place. On a phone, tap the answer choice first, then tap the sequence box.

Answer Choices
Label the vertices and name the polygon
Identify the number of sides of the polygon
Join all the points to form a closed figure
Mark points equal in number to the number of sides
Step Sequence
1
2
3
4
 

Key Terms

Poligon Vertex Side Diagonal Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Interior angle Exterior angle