Mensuration
MENSURATION
Basic Measurements
| Quantity | SI Unit | Common Conversions |
|---|---|---|
| Length | metre (m) | 1 km = 1000 m, 1 m = 100 cm |
| Weight | kilogram (kg) | 1 kg = 1000 g |
| Capacity | litre (L) | 1 L = 1000 mL |
| Time | second | 1 hr = 60 min = 3600 sec |
| Money | Rupee (₹) | 1 ₹ = 100 paise |
Memory Note: Capacity measures volume of liquid, expressed in L or mL.
Exam Tip: Always convert all quantities to the same unit before calculation.
Symmetry
| Type | Meaning | Example |
|---|---|---|
| Line Symmetry | Figure divides into two equal halves | Butterfly, Square |
| Rotational Symmetry | Looks same after rotation | Wheel, Square (4 times) |
Memory Note: Order of rotational symmetry = number of times a figure matches itself in one full rotation.
Exam Tip: A square has 4 lines of symmetry and rotational symmetry of order 4.
Perimeter of Plane Figures
| Shape | Formula |
|---|---|
| Square | 4 × side |
| Rectangle | 2(l + b) |
| Triangle | a + b + c |
| Circle | 2πr |
| Polygon | Sum of all sides |
Memory Note: Perimeter means total boundary length of a closed figure.
Exam Tip: Use π = 22/7 or 3.14 depending on calculation ease.
Area – Plane Figures
| Figure | Formula |
|---|---|
| Square | side² |
| Rectangle | length × breadth |
| Triangle | ½ × base × height |
| Circle | πr² |
| Parallelogram | base × height |
Memory Note: Area measures the region covered by a closed figure.
Exam Tip: Convert all lengths into same unit before area calculation.
Surface Area and Volume of 3D Figures
| Solid | Surface Area | Volume |
|---|---|---|
| Cube | 6a² | a³ |
| Cuboid | 2(lb + bh + lh) | l × b × h |
| Cylinder | 2πr(h + r) | πr²h |
| Sphere | 4πr² | 4/3 πr³ |
| Cone | πr(l + r) | 1/3 πr²h |
Memory Note: Volume is measured in cubic units like cm³ or m³.
Exam Tip: Always write units with your final numerical answer.
Combination and Conversion of Solids
| Case | Concept |
|---|---|
| Combination of Solids | Add or subtract volumes/surface areas |
| Conversion | Volume before = Volume after |
Memory Note: During conversion, volume remains constant but shape changes.
Exam Tip: Use volume conservation principle when converting one solid to another.