Perimeter of shapes
An ant walks once around the edge of your notebook cover. The distance it walks is the perimeter of the cover. A farmer puts a wire fence around a field – the wire length is also a perimeter.
The perimeter (परिमिती) of a shape is the total length of its boundary. It is measured in cm, m or km. For any shape: add the lengths of all sides.
In the figure : Regular triangle, pentagon and hexagon: perimeter = number of sides × side.
Rule 1: Add all sides — Perimeter = sum of all the sides.
- Easy : A triangle with sides 7, 9, 10 cm has perimeter 7 + 9 + 10 = 26 cm.
- Medium : A four-sided shape with sides 4, 6, 7, 9 cm has perimeter 26 cm.
- Exam-type : In a triangle of perimeter 24 cm two sides are 8 cm and 7 cm. Third side = 24 − 15 = 9 cm.
Rule 2: Regular shapes — All sides are equal, so perimeter = number of sides × one side.
- Easy : Equilateral triangle of side 12 cm: 3 × 12 = 36 cm.
- Medium : Regular pentagon of side 6 cm: 5 × 6 = 30 cm.
- Exam-type : Regular octagon of side 4 cm: 8 × 4 = 32 cm.
Perimeter is a length, so the unit is cm, m or km (not cm²).
Adding only two or three sides and forgetting one. Count the sides first and tick each one.
Memory clue: Perimeter = walk all the way round.
Spot the difference
| Shape | Perimeter |
|---|---|
| Triangle | a + b + c |
| Regular shape | sides × one side |
| Any shape | add all sides |
Practice questions
- 1Find the perimeter of a triangle with sides 7, 9 and 10 cm.
- 2Find the perimeter of a four-sided shape with sides 4, 6, 7, 9 cm.
- 3Find the perimeter of an equilateral triangle of side 12 cm.
- 4Find the perimeter of a regular pentagon of side 6 cm.
- 5Find the perimeter of a regular hexagon of side 5 cm.
- 6A triangle has perimeter 24 cm and two sides 8 cm and 7 cm. Find the third side.
- 7A regular octagon has side 4 cm. Find its perimeter.
- 8Asha added only 3 sides of a four-sided shape and got 20 cm. The fourth side is 6 cm. What is the real perimeter?
Show answers (try them yourself first)
- 126 cm
- 226 cm
- 336 cm
- 430 cm
- 530 cm
- 624 − (8 + 7) = 9 cm
- 78 × 4 = 32 cm
- 820 + 6 = 26 cm
Perimeter of rectangle and square
A school ground is a rectangle. To run one round, a player runs the length, breadth, length, breadth – two lengths and two breadths.
A rectangle has 2 equal lengths and 2 equal breadths, so perimeter = 2 × (length + breadth). A square has 4 equal sides, so perimeter = 4 × side.
In the figure : Rectangle 8 cm by 5 cm: perimeter 2 × (8 + 5) = 26 cm.
Rule 1: Rectangle — Perimeter = 2 × (l + b).
- Easy : Rectangle 12 cm by 7 cm: 2 × (12 + 7) = 2 × 19 = 38 cm.
- Medium : Park 80 m by 50 m: fence = 2 × 130 = 260 m.
- Exam-type : Perimeter 30 cm, length 9 cm: l + b = 15, so breadth = 15 − 9 = 6 cm.
Rule 2: Square — Perimeter = 4 × side. Side = perimeter ÷ 4.
- Easy : Square of side 9 cm: 4 × 9 = 36 cm.
- Medium : Square of perimeter 48 cm: side = 48 ÷ 4 = 12 cm.
- Exam-type : 4 rounds of a square ground of side 25 m: 4 × (4 × 25) = 400 m.
Perimeter of rectangle and square
In the app you can move this figure with your finger.
Open in the appFencing and walking round a field are perimeter problems.
Writing length + breadth only. You must double it: 2 × (l + b).
Memory clue: Rectangle: add two sides, double. Square: four sides.
Spot the difference
| Shape | Perimeter |
|---|---|
| Rectangle | 2 × (l + b) |
| Square | 4 × side |
| Side of a square | perimeter ÷ 4 |
Practice questions
- 1Find the perimeter of a rectangle 12 cm by 7 cm.
- 2Find the perimeter of a rectangle 15 cm by 10 cm.
- 3Find the perimeter of a square of side 9 cm.
- 4A square has perimeter 48 cm. Find its side.
- 5A park is 80 m long and 50 m wide. How long is the fence round it?
- 6A rectangle has perimeter 30 cm and length 9 cm. Find its breadth.
- 7A wire 40 cm long is bent into a square. Find the side.
- 8A boy runs 4 rounds of a square ground of side 25 m. How far does he run?
Show answers (try them yourself first)
- 138 cm
- 250 cm
- 336 cm
- 412 cm
- 5260 m
- 630 ÷ 2 = 15; 15 − 9 = 6 cm
- 740 ÷ 4 = 10 cm
- 84 × 100 = 400 m
Area by counting squares
Look at a chessboard. Count the small squares that cover it. The space covered on the board is its area. Area is the flat space inside a shape.
Area (क्षेत्रफळ) is the amount of flat surface a shape covers. It is counted in unit squares such as cm² or m². Two half squares make one whole square.
In the figure : 3 rows of 5 squares make 15 unit squares: area 15 cm².
Rule 1: Count the squares — Area = number of unit squares covered. For a rectangle: rows × squares in a row.
- Easy : 4 rows of 6 squares: 4 × 6 = 24 cm².
- Medium : 10 full squares and 4 half squares: 10 + 2 = 12 cm².
- Exam-type : 5 rows of 5 squares: 25 cm², which is a square shape.
Rule 2: Same area, different shapes — Different shapes can cover the same area.
- Easy : A 2 × 6 rectangle and a 3 × 4 rectangle both have area 12 cm².
- Medium : 1 m² = 100 cm × 100 cm = 10,000 cm².
- Exam-type : Square units are cm², m², km². The small 2 means "squares".
Area is measured in square units (cm², m²), perimeter in plain units (cm, m).
Writing the area in cm instead of cm².
Memory clue: Area = Aangan (courtyard) covered by squares.
Spot the difference
| Idea | Unit |
|---|---|
| Perimeter | cm, m |
| Area | cm², m² |
| Counting | unit squares |
Practice questions
- 14 rows of 6 unit squares: find the area.
- 25 rows of 5 unit squares: find the area.
- 3A shape has 10 full squares and 4 half squares. Find the area.
- 4Which unit is for area: cm or cm²?
- 5How many cm² make 1 m²?
- 6Draw two different rectangles with area 12 cm². Give their sides.
- 7A tile covers 1 cm². How many tiles cover 3 rows of 8?
- 8Asha says the area of a 3 × 4 rectangle is 12 cm because 3 × 4 = 12. What should she correct?
Show answers (try them yourself first)
- 124 cm²
- 225 cm²
- 310 + 2 = 12 cm²
- 4cm²
- 510,000
- 62 by 6 and 3 by 4.
- 724 tiles
- 8The unit: it is 12 cm², not cm.
Area of rectangle and square
A bedroom floor is 5 m long and 4 m wide. To lay square tiles, you need to know how many 1 m squares fit. Multiplying length and breadth gives the area.
Area of a rectangle = length × breadth. Area of a square = side × side. Missing side = area ÷ the known side.
In the figure : A 12 m by 8 m hall needs 96 ÷ 4 = 24 tiles of 2 m by 2 m.
Rule 1: Area formulae — Rectangle: l × b. Square: s × s.
- Easy : Rectangle 15 cm by 6 cm: 15 × 6 = 90 cm².
- Medium : Square of side 8 m: 8 × 8 = 64 m².
- Exam-type : Rectangle of area 72 cm² and length 9 cm: breadth = 72 ÷ 9 = 8 cm.
Rule 2: Tiles and L-shapes — Tiles = floor area ÷ area of one tile. L-shape: cut into rectangles or subtract the cut-out.
- Easy : Floor 10 m by 6 m = 60 m². Tile 2 m by 1 m = 2 m². Tiles = 60 ÷ 2 = 30.
- Medium : L-shape: 10 × 8 big rectangle minus 4 × 3 cut-out = 80 − 12 = 68 m².
- Exam-type : Floor 3 m by 3 m = 300 cm × 300 cm = 90,000 cm². Tile 30 cm × 30 cm = 900 cm². Tiles = 90,000 ÷ 900 = 100.
Area of rectangle and square
In the app you can move this figure with your finger.
Open in the appLength and breadth must be in the same unit before you multiply.
Adding instead of multiplying: area of 9 by 4 is 36 cm², not 13.
Memory clue: Area = Length × Breadth: Lay the rows.
Spot the difference
| Shape | Area |
|---|---|
| Rectangle | l × b |
| Square | s × s |
| Tiles needed | floor ÷ tile |
Practice questions
- 1Find the area of a rectangle 15 cm by 6 cm.
- 2Find the area of a square of side 8 m.
- 3A rectangle has area 72 cm² and length 9 cm. Find the breadth.
- 4A floor is 10 m by 6 m. How many tiles of 2 m by 1 m cover it?
- 5A square has area 49 cm². Find its side.
- 6Find the area of an L-shape made of a 10 m × 8 m rectangle with a 4 m × 3 m corner cut out.
- 7A 3 m by 3 m floor is covered with square tiles of side 30 cm. How many tiles?
- 8Ravi finds the area of a 9 cm by 4 cm rectangle as 9 + 4 = 13. Correct him.
Show answers (try them yourself first)
- 190 cm²
- 264 m²
- 38 cm
- 460 ÷ 2 = 30
- 57 cm (7 × 7 = 49)
- 680 − 12 = 68 m²
- 790,000 ÷ 900 = 100 tiles
- 8Multiply: 9 × 4 = 36 cm².
Perimeter and area problems
A gardener puts a fence around a garden and plants grass inside it. The fence is a perimeter job and the grass is an area job. Choosing the right idea is half the answer.
Fence, border, ribbon, boundary: use perimeter. Tiles, carpet, paint, grass: use area. For cost: find perimeter or area first, then multiply by the rate.
In the figure : The same perimeter 16 cm can give areas 12 cm² and 16 cm².
Rule 1: Perimeter or area? — Ask: is it around the edge (perimeter) or covering the surface (area)?
- Easy : Fence round a 20 m by 15 m garden: 2 × 35 = 70 m.
- Medium : Carpet for an 8 m by 5 m room: 8 × 5 = 40 m².
- Exam-type : Paint a 6 m by 3 m wall: 18 m².
Rule 2: Cost problems — Cost = perimeter or area × rate.
- Easy : Fence 70 m at ₹ 12 per metre = 70 × 12 = ₹ 840.
- Medium : Carpet 40 m² at ₹ 50 per m² = ₹ 2,000.
- Exam-type : Paint 18 m² at ₹ 15 per m² = ₹ 270.
Same perimeter does not mean same area: a 7 × 3 rectangle and a 5 × 5 square both have perimeter 20 cm, but areas 21 and 25 cm².
Using area for a fence, or perimeter for tiles. Check the words in the question.
Memory clue: Fence, frame, ribbon → perimeter. Tile, carpet, paint → area.
Spot the difference
| Job | Use |
|---|---|
| Fence | perimeter |
| Carpet | area |
| Cost | amount × rate |
Practice questions
- 1Perimeter or area: a fence round a field?
- 2Perimeter or area: paint on a wall?
- 3Perimeter or area: lace round a handkerchief?
- 4Find the fence length for a 20 m by 15 m garden.
- 5Find the cost of fencing 70 m at ₹ 12 per metre.
- 6Carpet costs ₹ 50 per m². Find the cost for an 8 m by 5 m room.
- 7A 6 m by 3 m wall is painted at ₹ 15 per m². Find the cost.
- 8A 9 × 3 rectangle and a 6 × 6 square both have perimeter 24 cm. Which has the bigger area and by how much?
Show answers (try them yourself first)
- 1Perimeter
- 2Area
- 3Perimeter
- 470 m
- 5₹ 840
- 640 × 50 = ₹ 2,000
- 718 × 15 = ₹ 270
- 8Square: 36 cm² against 27 cm²; larger by 9 cm².