Perimeter

Class 6 Maths · Chapter 6: Perimeter and Area · NCERT Ganita Prakash section 6.1

Learn

The perimeter of a closed shape is the distance all the way around its boundary, going round once. Let us walk around this rectangle. Each small square has sides of 1 cm.

Walk along the top: 5 cm. Then down the right side: 3 cm. So far 5 + 3 = 8 cm.

5 + 3 = 8 cm

Along the bottom (5 cm) and up the left side (3 cm), and we are back at the start. Length and breadth each come twice.

5 + 3 + 5 + 3 = 2 × (5 + 3) = 16 cm

Rectangle ABCD is 9 cm long and 6 cm wide. Opposite sides of a rectangle are equal (AB = CD, BC = AD), so perimeter of a rectangle = 2 × (length + breadth).

2 × (9 + 6) = 2 × 15 = 30 cm

Aditi sticks ribbon all around a square greeting card with sides of 20 cm. All 4 sides of a square are equal, so instead of adding we multiply: perimeter of a square = 4 × side.

4 × 20 cm = 80 cm of ribbon

For a triangle, add its three sides. A triangle with sides 6 cm, 8 cm and 9 cm has perimeter 23 cm.

6 + 8 + 9 = 23 cm

Regular polygons have all sides equal, like the equilateral triangle. So perimeter = number of sides × length of one side.

Kabir jogs 4 rounds of a square ground with sides of 60 m. One round is the perimeter: 4 × 60 = 240 m. Four rounds: 4 × 240 = 960 m.

4 × 240 m = 960 m

Your turn! Change the length and breadth. The coral line is the perimeter. Can you complete the mission?

Remember

• Perimeter of a polygon = sum of all its sides.
• Rectangle: 2 × (length + breadth). Square: 4 × side. Equilateral triangle: 3 × side.

Quick check

A rectangle is 7 cm long and 3 cm wide. What is its perimeter?

1. 10 cm
2. 20 cm
3. 21 cm
4. 21 sq cm

Think about it

A square and a rectangle both have a perimeter of 24 cm. The rectangle is 8 cm long. Which shape covers more space?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.