Class 5 - Polygons - Complete Learning Guide

Polygons are one of the most important topics in elementary geometry is polygons. In this lesson, we will learn about polygons, their types with solved practice questions for class 5 students.

Table of Contents

• What is a Polygon?
• Types of Polygons
• Regular vs Irregular Polygons
• Solved Examples on Polygons for Class 5
• Practice Questions on Polygons for Class 5
• Polygons Worksheet for Class 5

What is a Polygon?

A polygon is a closed shape made up of straight lines. These straight lines are called sides. The corners where two sides meet are called vertices (or angles).

• Closed Shape: It must be completely closed with no gaps
• Straight Sides: All sides must be straight lines (not curved)
• At least 3 sides: The smallest polygon has 3 sides
• Vertices: Points where two sides meet
• Side: A straight line that forms the edge of the polygon
• Vertex: A corner point where two sides meet
• Angle: The space between two sides at a vertex

Types of Polygons

The Types of Polygons Based on Number of Sides

Name	Number of Sides	Example
Triangle	3 sides	A three-cornered shape
Quadrilateral	4 sides	A square or rectangle
Pentagon	5 sides	A five-sided shape
Hexagon	6 sides	A six-sided shape
Heptagon	7 sides	A seven-sided shape
Octagon	8 sides	A stop sign shape

Regular vs Irregular Polygons

• Regular Polygon: All sides are equal and all angles are equal
• Irregular Polygon: Sides and angles are not all equal

Solved Examples on Polygons for Class 5

Example 1: Identifying a Polygon

Question: Is a triangle a polygon? Explain why or why not.

Solution: Yes, a triangle is a polygon.

• It has 3 straight sides
• It is a closed shape
• It has 3 vertices
• It meets all the requirements of a polygon

Answer: Yes, a triangle is a polygon because it is a closed shape with 3 straight sides.

Example 2: Counting Sides and Vertices

Question: A square has how many sides and vertices?

Solution: A square is a 4 sided polygon.

• Number of sides = 4
• Number of vertices = 4

In any polygon, the number of sides equals the number of vertices.

Answer: A square has 4 sides and 4 vertices.

Example 3: Finding the Name of a Polygon

Question: What is the name of a polygon with 6 sides?

Solution: A polygon with 6 sides is called a hexagon.

Answer: A hexagon has 6 sides.

Example 4: Regular Polygon Properties

Question: Is a rectangle a regular polygon?

Solution: No, a rectangle is not a regular polygon.

• In a regular polygon, all sides must be equal in length
• In a regular polygon, all angles must be equal
• A rectangle has opposite sides equal (not all sides equal)
• Therefore, a rectangle is an irregular polygon

Answer: No, a rectangle is not a regular polygon because not all its sides are equal in length.

Example 5: Identifying Non Polygons

Question: Is a circle a polygon? Explain.

Solution: No, a circle is not a polygon.

• A polygon must have straight sides
• A circle has a curved side
• Polygons must have vertices (corners)
• A circle has no corners or vertices
• Therefore, a circle is not a polygon

Answer: No, a circle is not a polygon because it has curved sides, not straight sides.

Example 6: Polygon Vertices Formula

Question: If a polygon has 8 sides, how many vertices does it have?

Solution: In any polygon: Number of sides = Number of vertices

If sides = 8 Then vertices = 8

Answer: A polygon with 8 sides has 8 vertices.

Example 7: Identifying Polygon Types

Question: Name the polygon that has 5 equal sides and 5 equal angles.

Solution: A polygon with 5 equal sides and 5 equal angles is a regular pentagon.

• Pentagon = 5 sides
• Regular = all sides equal and all angles equal

Answer: A regular pentagon has 5 equal sides and 5 equal angles.

Example 8: Real-World Polygon Recognition

Question: Is a stop sign a polygon? What type?

Solution: Yes, a stop sign is a polygon.

• It has 8 straight sides
• It is a closed shape
• It has 8 vertices
• This is called an octagon

Answer: Yes, a stop sign is a regular octagon (8-sided polygon).

Example 9: Sides and Angles Relationship

Question: How many angles does a quadrilateral have?

Solution: A quadrilateral has 4 sides.

Every polygon has as many angles as it has sides.

Number of sides = 4 Number of angles = 4

Answer: A quadrilateral has 4 angles.

Example 10: Comparing Polygons

Question: Which has more sides - a pentagon or a hexagon? How many more?

Solution: Pentagon = 5 sides Hexagon = 6 sides

Difference = 6 - 5 = 1 side

Hexagon has more sides.

Answer: A hexagon has 1 more side than a pentagon.

Practice Questions on Polygons for Class 5

1: Which of the following is a polygon?

• (A) Circle
• (B) Triangle
• (C) Oval
• (D) Both B and C

2: How many sides does a pentagon have?

• (A) 4 sides
• (B) 5 sides
• (C) 6 sides
• (D) 7 sides

3: What is a regular polygon?

• (A) A polygon with curved sides
• (B) A polygon with all equal sides and angles
• (C) A polygon with only 3 sides
• (D) A polygon that is not closed

4: What is the name of a 6-sided polygon?

• (A) Heptagon
• (B) Pentagon
• (C) Hexagon
• (D) Octagon

5: How many vertices does a quadrilateral have?

• (A) 3 vertices
• (B) 4 vertices
• (C) 5 vertices
• (D) 6 vertices

6: A polygon must have straight sides.

• (A) True
• (B) False

7: A circle is a polygon because it is a closed shape.

• (A) True
• (B) False

8: Every polygon has the same number of sides and vertices.

• (A) True
• (B) False

9: A square is a regular polygon.

• (A) True
• (B) False

10: An octagon has 8 sides and 8 angles.

• (A) True
• (B) False

11: How many sides does a triangle have? Is it a polygon?

12: What is the difference between a regular polygon and an irregular polygon? Give an example of each.

13: A polygon has 7 sides. What is its name? How many vertices does it have?

14: Describe what makes a shape a polygon using at least 3 key features.

15: Draw and label a pentagon. Show its sides and vertices.

Formula : Sides = Vertices = Angles (in any polygon)

Polygons Worksheet for Class 5

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