What this chapter is about
This chapter teaches you two ways to measure flat shapes. The first is perimeter, which means the total length of the boundary around a shape. The second is area, which means how much surface a shape covers.
You already know how to measure length with a ruler. Now you will use that skill to find how much fencing goes around a garden or how many tiles fit on a floor. These ideas help in daily life — buying border tape for a chart, painting a wall, or laying a carpet.
After this chapter, you should be able to find the perimeter and area of squares, rectangles and simple combined shapes. You should also understand the difference between the two ideas clearly.
Key ideas
- Perimeter is the total distance around a closed shape. You add up all the side lengths.
- Area is the amount of flat surface inside a shape. We measure it in square units like square centimetres (cm²) or square metres (m²).
- For a rectangle, perimeter = 2 × (length + breadth). Area = length × breadth.
- For a square, perimeter = 4 × side. Area = side × side.
- Two shapes can have the same perimeter but different areas, or the same area but different perimeters.
- To find the area of an irregular shape drawn on a square grid, count the full squares and estimate the part squares.
- Perimeter is measured in simple length units (cm, m). Area is measured in square units (cm², m²).
Formulas and facts to remember
- Shape: Rectangle · Perimeter: 2 × (length + breadth) · Area: length × breadth
- Shape: Square · Perimeter: 4 × side · Area: side × side
- 1 metre = 100 centimetres, so 1 m² = 10 000 cm².
- Perimeter tells you "how long is the boundary."
- Area tells you "how much space is covered."
Worked examples
### Example 1: Finding perimeter and area of a rectangle
Rina has a rectangular chart paper. Its length is 50 cm and breadth is 30 cm. Find the perimeter and area.
Perimeter Perimeter = 2 × (length + breadth) = 2 × (50 + 30) = 2 × 80 = 160 cm
Area Area = length × breadth = 50 × 30 = 1500 cm²
So Rina needs 160 cm of ribbon to go around the chart, and the chart covers 1500 square centimetres.
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### Example 2: Finding the side of a square from its perimeter
A square park has a perimeter of 120 metres. Find the length of one side.
Perimeter of a square = 4 × side 120 = 4 × side side = 120 ÷ 4 side = 30 m
Each side of the park is 30 metres long.
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### Example 3: Comparing two rectangles
Rectangle A has length 8 m and breadth 2 m. Rectangle B has length 5 m and breadth 4 m.
Which has the greater area?
Area of A = 8 × 2 = 16 m² Area of B = 5 × 4 = 20 m²
Rectangle B has the greater area even though both shapes look different.
Common mistakes
- Confusing perimeter and area → Remember: perimeter is the boundary (add sides), area is the inside (multiply length and breadth).
- Writing the unit for area as "cm" instead of "cm²" → Area is always in square units because you multiply two lengths.
- Forgetting to multiply by 2 in the rectangle perimeter formula → A rectangle has two lengths and two breadths, so you must double the sum.
- Thinking same perimeter means same area → Two shapes with equal perimeter can cover different amounts of space.
- Using different units for length and breadth without converting → Always convert to the same unit (both in cm or both in m) before calculating.
Quick revision
- Perimeter = total length of all sides around a shape.
- Area = space covered inside a shape, measured in square units.
- Rectangle: Perimeter = 2 × (l + b), Area = l × b.
- Square: Perimeter = 4 × side, Area = side × side.
- Same perimeter does not mean same area.
- Always write area with a "²" in the unit.