Area

Class 6 Maths · Chapter 6: Perimeter and Area · NCERT Ganita Prakash section 6.2

Learn

The area of a closed shape is the amount of region it covers. We measure it with unit squares: a square with sides of 1 cm has an area of 1 sq cm.

Fill the first row: it has 5 squares.

Fill all the rows: 3 rows of 5 = 15 squares. Instead of counting, multiply! Area of a rectangle = length × breadth.

5 × 3 = 15 sq cm

A square has 4 rows of 4 when its side is 4 cm. Area of a square = side × side. Remember: perimeter is a length (cm), area is a number of squares (sq cm).

4 × 4 = 16 sq cm

A wall is 6 m long and 3 m high. It has a window 2 m wide and 1 m high. Area to paint = area of wall − area of window.

18 − 2 = 16 sq m

Some shapes are not rectangles. Split them into rectangles, find each area, and add. Here A is 3 × 5 and B is 3 × 2.

15 + 6 = 21 sq m

For curved shapes, use squared paper: a full square counts 1, more than half counts 1, less than half is left out, and exactly half counts ½. This circle (4 units across) comes to about 12 sq units.

4 full + 8 more than half ≈ 12 sq units

Same area does not mean same perimeter! These rectangles all have area 12 sq units. The closer a rectangle is to a square, the smaller its perimeter.

Your turn! Make a rectangle with area 12 sq cm. Try to find two different ones, and see how the perimeter changes.

Remember

• Area is the amount of region a closed shape covers. It is measured in square units (sq cm, sq m).
• Rectangle: length × breadth. Square: side × side.
• Split other shapes into rectangles, find each area, then add.

Quick check

A room is 6 m long and 4 m wide. What is the area of its floor?

1. 10 sq m
2. 20 m
3. 24 sq m
4. 24 m

Think about it

Make rectangles with whole-number sides and area 24 sq units. Which has the greatest perimeter? Which has the least?

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.