Mensuration
Area, Surface Area and Volume of Solids
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Overview
Mensuration is the branch of mathematics dealing with measurement of geometric figures — their lengths, areas and volumes. For OTET Paper II, this topic carries significant weight as it tests both conceptual understanding and computational accuracy. Questions typically involve calculating area of plane figures, surface area of 3D solids and volume of common solids.
This topic connects directly to real-life applications like calculating land area, paint required for walls, water capacity of tanks and material needed for construction. Students at upper primary level must transition from 2D thinking (area, perimeter) to 3D visualization (surface area, volume). Mastery requires memorizing key formulas and understanding when to apply each.
Expect 2-4 questions from this topic, often presented as word problems involving composite figures or unit conversions. Speed and formula recall are essential.
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Key Concepts
- **Area** measures the surface enclosed by a 2D figure, expressed in square units (cm², m²).
- **Perimeter** is the total boundary length of a plane figure, expressed in linear units.
- **Surface area** of a 3D solid is the total area of all its faces — think of it as the amount of material needed to wrap the solid completely.
- **Lateral (curved) surface area** excludes the top and bottom faces — useful when calculating material for the curved portion only (like labeling a cylindrical can).
- **Total surface area** includes all faces — lateral surface plus the area of bases.
- **Volume** measures the space occupied by a 3D solid, expressed in cubic units (cm³, m³, litres).
- **Capacity** often refers to the volume of liquids a container can hold; 1 litre = 1000 cm³.
- For composite solids, break them into simpler shapes, calculate separately, then add or subtract as needed.
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Formulas / Key Facts
### Plane Figures (Area and Perimeter)
| Figure | Area | Perimeter | |--------|------|-----------| | Rectangle | l × b | 2(l + b) | | Square | a² | 4a | | Triangle | ½ × base × height | Sum of all sides | | Right triangle | ½ × base × perpendicular | a + b + c | | Equilateral triangle | (√3/4) × a² | 3a | | Parallelogram | base × height | 2(a + b) | | Rhombus | ½ × d₁ × d₂ | 4a | | Trapezium | ½ × (a + b) × h | Sum of all sides | | Circle | πr² | 2πr (circumference) | | Semicircle | ½πr² | πr + 2r |
### 3D Solids (Surface Area and Volume)