Polygons
A polygon is a closed flat shape made of straight line segments. You already know triangles (3 sides) and quadrilaterals (4 sides). In Class 4, you learn about polygons with 5, 6, 7, and 8 sides and their properties.
Polygons are found everywhere — the shape of a STOP sign (octagon), a honeycomb cell (hexagon), a football panel (pentagon), and tiles on a floor.
What is Polygons - Class 4 Maths (Geometry)?
A polygon is a 2D closed shape with:
- Straight sides (no curves).
- Sides that do not cross each other.
- At least 3 sides.
Naming polygons by number of sides:
| Sides | Name | Example |
|---|---|---|
| 3 | Triangle | Slice of pizza |
| 4 | Quadrilateral | Notebook, window |
| 5 | Pentagon | Star shape base |
| 6 | Hexagon | Honeycomb, nut bolt |
| 7 | Heptagon | Some coins |
| 8 | Octagon | STOP sign |
Regular polygon: All sides equal and all angles equal. Irregular polygon: Sides or angles are not all equal.
Solved Examples
Example 1: Example 1: Identifying a Pentagon
Problem: A shape has 5 straight sides. What is it called?
Solution:
A shape with 5 sides is called a pentagon.
Answer: Pentagon
Example 2: Example 2: Identifying a Hexagon
Problem: Count the sides of a honeycomb cell. What polygon is it?
Solution:
A honeycomb cell has 6 sides → it is a hexagon.
Answer: Hexagon
Example 3: Example 3: Regular vs Irregular
Problem: A quadrilateral has sides 4 cm, 4 cm, 4 cm, 4 cm and all angles 90°. Is it regular?
Solution:
All sides are equal and all angles are equal (90°).
Answer: Yes, it is a regular quadrilateral (a square).
Example 4: Example 4: Number of Corners
Problem: How many corners (vertices) does an octagon have?
Solution:
The number of corners equals the number of sides.
Answer: An octagon has 8 corners.
Example 5: Example 5: Perimeter of a Regular Pentagon
Problem: A regular pentagon has each side measuring 6 cm. Find its perimeter.
Solution:
Perimeter = 5 x 6 = 30 cm
Answer: Perimeter = 30 cm
Example 6: Example 6: Diagonals
Problem: How many diagonals does a hexagon have?
Solution:
Formula: Number of diagonals = n(n-3) ÷ 2, where n = number of sides.
For hexagon: 6(6-3) ÷ 2 = 6 x 3 ÷ 2 = 9
Answer: A hexagon has 9 diagonals.
Example 7: Example 7: Is it a Polygon?
Problem: Is a circle a polygon?
Solution:
A polygon must have straight sides. A circle has a curved boundary, not straight sides.
Answer: No, a circle is not a polygon.
Example 8: Example 8: Angle Sum
Problem: Find the sum of angles in a pentagon.
Solution:
Formula: Sum of angles = (n − 2) x 180°, where n = number of sides.
For pentagon: (5 − 2) x 180° = 3 x 180° = 540°
Answer: Sum of angles in a pentagon = 540°
Example 9: Example 9: Word Problem
Problem: Meera is making a rangoli using a regular hexagon. Each side is 8 cm. She outlines it with coloured tape. How much tape does she need?
Solution:
Perimeter of regular hexagon = 6 x 8 = 48 cm
Answer: Meera needs 48 cm of tape.
Example 10: Example 10: Naming by Sides
Problem: Name the polygons with 3, 5, and 8 sides.
Solution:
3 sides → Triangle
5 sides → Pentagon
8 sides → Octagon
Answer: Triangle, Pentagon, Octagon
Key Points to Remember
- A polygon is a closed shape made of straight line segments.
- Polygons are named by the number of sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8).
- The number of vertices = number of sides.
- A regular polygon has all sides and all angles equal.
- Sum of angles = (n − 2) x 180°.
- A shape with curved sides is not a polygon.
Practice Problems
- Name the polygon with 7 sides.
- How many vertices does a pentagon have?
- A regular octagon has each side of 5 cm. Find its perimeter.
- Find the sum of angles in a hexagon.
- Is a shape with 2 straight sides a polygon? Why or why not?
- Draw a regular hexagon and an irregular hexagon.
- How many diagonals does a pentagon have?
Frequently Asked Questions
Q1. What is a polygon?
A polygon is a closed 2D shape made of straight line segments. It must have at least 3 sides, and the sides must not cross each other.
Q2. How are polygons named?
By the number of sides: 3 = triangle, 4 = quadrilateral, 5 = pentagon, 6 = hexagon, 7 = heptagon, 8 = octagon, 9 = nonagon, 10 = decagon.
Q3. What is the difference between regular and irregular polygons?
A regular polygon has all sides equal and all angles equal. An irregular polygon has sides or angles of different sizes. A square is regular; a rectangle is irregular (sides are not all equal).
Q4. Is a circle a polygon?
No. A polygon must have straight sides. A circle is a curved shape, so it is not a polygon.
Q5. How do you find the perimeter of a regular polygon?
Multiply the side length by the number of sides. For example, a regular hexagon with sides of 5 cm has a perimeter of 6 x 5 = 30 cm.
Q6. What is a diagonal?
A diagonal is a line segment connecting two non-adjacent vertices of a polygon. A triangle has 0 diagonals, a quadrilateral has 2, and a pentagon has 5.
Q7. What is the sum of angles in a quadrilateral?
360°. Using the formula (n-2) x 180°: (4-2) x 180° = 360°.
Q8. Are polygons covered in NCERT Class 4?
Yes, identifying and naming common polygons is part of the CBSE/NCERT Class 4 Maths curriculum under the Geometry chapter.
