Quick Revision Notes – Mensuration
🔹 Plane Figures
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Closed 2D (two-dimensional) shapes are called plane figures.
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The boundary of a figure is called its perimeter.
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The surface enclosed by the boundary is called its area.
🟨 Perimeter
🧭 Definition
Perimeter = Length of the boundary of a closed figure.
👉 For figures made of straight lines:
Perimeter = Sum of lengths of all sides
📏 Formulas
| Shape | Formula for Perimeter | Example |
|---|---|---|
| Rectangle | 2 × (Length + Breadth) | If L = 16 m, B = 12 m → Perimeter = 2 × (16 + 12) = 56 m |
| Square | 4 × Side | Side = 25 cm → Perimeter = 4 × 25 = 100 cm |
| Equilateral Triangle | 3 × Side | Side = 13 cm → Perimeter = 3 × 13 = 39 cm |
| Regular Pentagon | 5 × Side | Side = 9 cm → Perimeter = 5 × 9 = 45 cm |
| Regular Hexagon | 6 × Side | Side = 15 cm → Perimeter = 6 × 15 = 90 cm |
| Regular Octagon | 8 × Side | Side = 7 cm → Perimeter = 8 × 7 = 56 cm |
💰 Application Example
Find the cost of fencing a rectangular field
→ Cost = Perimeter × Rate per meter
Example:
Length = 24 m, Breadth = 18 m, Rate = ₹8/m
Perimeter = 2 × (24 + 18) = 84 m
Cost = 84 × 8 = ₹672
🟦 Regular Closed Figures
Figures with equal sides and equal angles are called Regular Polygons.
👉 Examples: Square, Equilateral Triangle, Regular Pentagon, Regular Hexagon, etc.
Formula:
Perimeter of Regular Polygon = Number of sides × Length of one side
🟥 Area
🧭 Definition
Area = Surface enclosed by the boundary of a closed figure.
Unit of area = sq. units (cm², m², etc.)
Formulas
| Shape | Formula for Area | Example |
|---|---|---|
| Rectangle | Area = Length × Breadth | 20 cm × 12 cm = 240 cm² |
| Square | Area = Side × Side | 13 cm × 13 cm = 169 cm² |
When Area is Given
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To Find Length:
Length = Area ÷ BreadthExample: Area = 48 m², Breadth = 6 m
→ Length = 48 ÷ 6 = 8 m -
To Find Breadth:
Breadth = Area ÷ LengthExample: Area = 81 m², Length = 9 m
→ Breadth = 81 ÷ 9 = 9 m
📐 Area of Irregular Figures
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Place the figure on graph paper with 1 cm × 1 cm squares.
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Count:
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Full squares = 1 sq. unit each
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Half squares = ½ sq. unit each
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Add them to estimate total area.
Example:
Full squares = 32, Half squares = 21
Area = (32 × 1) + (21 × ½) = 32 + 10.5 = 42.5 sq. units
🧮 Summary of Important Formulas
| Shape | Perimeter | Area |
|---|---|---|
| Rectangle | 2 × (L + B) | L × B |
| Square | 4 × Side | Side × Side |
| Equilateral Triangle | 3 × Side | – |
| Regular Pentagon | 5 × Side | – |
| Regular Hexagon | 6 × Side | – |
| Regular Octagon | 8 × Side | – |
✅ Remember
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Perimeter = Distance around a figure.
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Area = Space inside a figure.
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Always write units properly → cm, m for perimeter and cm², m² for area.
Attend Question Paper Here:
Class 6 Mensuration Practice Paper | Extra Questions Worksheet
