Perimeter and Area
How far is it around a shape, and how much surface does it cover? This Class 6 Ganita Prakash chapter answers both: perimeter is the distance around a closed figure, and area is the amount of surface inside it. Students learn the perimeter of common shapes and the area of rectangles and squares.
Learning objectives
- Find the perimeter of rectangles, squares and triangles.
- Measure area by counting unit squares.
- Use the area formulas for a rectangle and a square.
- Apply perimeter and area to simple real-life problems.
Key concepts
Perimeter
The perimeter of a closed figure is the total distance around its boundary, found by adding the lengths of all its sides. For a rectangle this is 2 × (length + breadth), and for a square with equal sides it is 4 × side. Perimeter is measured in units of length such as cm or m.
Area by counting squares
Area is the amount of surface a flat shape covers, measured in square units. One way to find it is to place the shape on squared paper and count the unit squares inside, counting a square that is more than half covered as one and ignoring one less than half covered.
Area of a rectangle and square
Counting can be replaced by a formula. The area of a rectangle is length × breadth, and the area of a square is side × side. Area is always written in square units, such as cm² or m².
Using perimeter and area
These ideas solve everyday problems: the length of fencing needed around a field is a perimeter, while the amount of tiles or grass to cover it is an area. The two are different and use different units, so they should not be mixed up.
Important formulas
Perimeter of rectangle
P = 2 × (length + breadth)
Perimeter of square
P = 4 × side
Area of rectangle
A = length × breadth
Area of square
A = side × side
Key definitions
- Perimeter
- The total distance around the boundary of a closed figure.
- Area
- The amount of surface a flat shape covers, in square units.
- Unit square
- A square of side 1 unit, used to measure area.
- Square unit
- The unit of area, such as cm² or m².
Solved examples
Q1. Find the perimeter of a rectangle 8 cm long and 3 cm wide.
Solution: P = 2 × (8 + 3) = 2 × 11 = 22 cm.
Q2. Find the area of a square of side 6 cm.
Solution: A = 6 × 6 = 36 cm².
Q3. A rectangle has area 24 cm² and length 6 cm. Find its breadth.
Solution: Breadth = area ÷ length = 24 ÷ 6 = 4 cm.
Common mistakes to avoid
- Mixing up perimeter (length units) with area (square units).
- Using 'add the sides' for area instead of multiplying.
- Forgetting to double (length + breadth) for a rectangle's perimeter.
- Leaving out the square unit (cm²) when writing an area.
Perimeter and Area — MCQ Quiz
10 questions with instant feedback. Use number keys 1–4 to answer.
The distance around a closed figure is its:
Practice questions
Short answer
How do you find the perimeter of a rectangle?
Add length and breadth and double the result: 2 × (length + breadth).
In what units is area measured?
In square units, such as cm² or m².
What is the area of a square of side 10 cm?
10 × 10 = 100 cm².
Long answer
Explain the difference between perimeter and area, with an example.
Perimeter is the distance all the way around a shape's boundary and is measured in units of length, while area is the surface the shape covers and is measured in square units. For a rectangle 5 cm by 3 cm, the perimeter is 2 × (5 + 3) = 16 cm, and the area is 5 × 3 = 15 cm². The two answers describe different things — one is how far it is around, the other how much it covers — so they use different units and must not be confused.
A rectangular garden is 12 m long and 5 m wide. Find the length of fencing needed and the area to be covered with grass.
Fencing runs around the boundary, so it is the perimeter: 2 × (12 + 5) = 2 × 17 = 34 m. The grass covers the inside surface, so it is the area: 12 × 5 = 60 m². The gardener therefore needs 34 m of fencing and enough grass for 60 m².
HOTS (Higher Order Thinking)
Two rectangles have the same area of 24 cm² but different perimeters. Give an example.
A 6 cm × 4 cm rectangle has perimeter 20 cm, while a 12 cm × 2 cm rectangle (same area 24 cm²) has perimeter 28 cm.
If the side of a square is doubled, how does its area change?
The area becomes four times as large, because area = side × side, and doubling each side multiplies the product by 2 × 2 = 4.
Quick revision
Revision notes
- Perimeter = distance around (length units); area = surface inside (square units).
- Rectangle: P = 2(l + b), A = l × b.
- Square: P = 4 × side, A = side × side.
- Triangle perimeter = sum of three sides.
Key takeaways
- Perimeter and area answer different questions.
- Area of a rectangle is length × breadth.
- Always state area in square units.
Frequently asked questions
What is perimeter?
The total distance around the boundary of a closed figure.
How is the area of a rectangle found?
By multiplying its length by its breadth.
Why is area measured in square units?
Because it counts unit squares, each one unit by one unit.