Perimeter and Area | Mathematics Grade 6 CBSE

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The six ideas of perimeter & area

Perimeter is about the boundary; area is about the surface inside. Tap each term to see what it means, its formula, and the unit it uses.

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The three big ideas

Perimeter is the total length of the boundary of a closed flat shape. To find it for any shape, just add the lengths of all its sides.
Rectangle: opposite sides are equal, so perimeter = length + breadth + length + breadth = 2 × (length + breadth).
Square: all four sides are equal, so perimeter = side + side + side + side = 4 × side.
Perimeter is a length, so it is measured in length units — centimetres (cm), metres (m), kilometres (km).

Worked example. A rectangular playground is 30 m long and 20 m wide. How much fencing is needed to go all the way around it?

Fencing follows the boundary, so we need the perimeter.

Perimeter = 2 × (length + breadth) = 2 × (30 + 20) = 2 × 50 = 100 m of fencing.

Common mistake: using only two sides — for example writing 30 + 20 = 50 m. A rectangle has four sides, so you must count both lengths and both breadths.

Area is the amount of flat surface a shape covers. One way to measure it is to cover the shape with equal unit squares and count them.
A unit square that is 1 cm on each side has an area of 1 square centimetre (1 cm²); one that is 1 m on each side has an area of 1 m².
To estimate the area of an odd shape drawn on squared paper: count every fully covered square as 1, count a square that is more than half covered as 1, count a square less than half covered as 0, and count a half square as ½.
Area is always measured in square units (cm², m², km²) — never in plain cm or m.

Worked example. A shape drawn on cm-squared paper covers 14 full squares, 6 squares that are more than half filled, and 4 squares that are less than half filled. Estimate its area.

Full squares: count as 14. More-than-half squares: count each as 1 → 6. Less-than-half squares: count as 0.

Estimated area = 14 + 6 + 0 = 20 cm² (approximately).

Common mistake: writing the answer as "20 cm". Area must carry a square unit — the correct answer is 20 cm².

For a rectangle, the unit squares line up in neat rows. If it is 5 cm long and 3 cm wide, there are 3 rows of 5 squares = 15 squares — so Area of a rectangle = length × breadth.
A square is a rectangle with equal sides, so Area of a square = side × side.
This shortcut saves counting every square — but it works only when length and breadth are in the same unit. Convert first if they differ.
Remember the contrast: perimeter adds the sides (a length), while area multiplies them (a surface).

Worked example. A room floor is 6 m long and 4 m wide. How many square metres of tiles are needed to cover it, and what length of skirting runs around its edge?

Tiles cover the surface → use area: Area = length × breadth = 6 × 4 = 24 m² of tiles.

Skirting runs along the boundary → use perimeter: 2 × (6 + 4) = 2 × 10 = 20 m.

Common mistake: mixing up the formulas. 2 × (l + b) gives the perimeter (boundary); l × b gives the area (surface). Ask yourself: am I going around the shape or covering it?

Where you'll meet it

Perimeter & area at work

Fencing a field

A farmer near Nashik buys wire to fence a rectangular plot. The wire must follow the boundary, so the length to buy is the perimeter — get it wrong and there is either a gap or wasted wire.

Tiling and painting

To tile a floor or paint a wall, you need to cover a surface — that is an area calculation. A shop sells tiles by the square metre, so length × breadth tells you how many to order.

Cloth and borders

A tailor uses area to know how much cloth a tablecloth needs, and perimeter to know how much lace to stitch around its edge — two different measurements for the same piece.

Check yourself

Competency quiz

Modelled on the competency-based pattern — MCQ, assertion–reason and a case study, testing whether you can use the ideas, not just recall them.

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