Mensuration
Area, Surface Area and Volume of 2D/3D Figures
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Overview
Mensuration is the branch of mathematics dealing with measurement of geometric figures — their lengths, areas and volumes. For TN TET Paper II, this topic carries significant weight as it tests both conceptual understanding and computational accuracy. Questions typically involve direct formula application, word problems requiring identification of appropriate shapes, and comparison problems.
Students must master two broad categories: **2D figures** (area and perimeter) and **3D figures** (surface area and volume). The syllabus expects familiarity with standard shapes taught in classes 6-8: rectangles, triangles, circles, parallelograms, trapeziums, cubes, cuboids, cylinders, cones and spheres. Real-life application questions — finding the cost of painting a wall, volume of a water tank, material needed for a box — are common.
Success requires memorising formulas accurately, understanding when each applies, and careful unit conversion. Careless errors in squaring, cubing or forgetting to convert cm to m are frequent pitfalls.
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Key Concepts
- **Perimeter** is the total length of the boundary of a 2D figure; **area** is the region enclosed within that boundary.
- **Surface area** of a 3D object is the total area of all its outer faces. It comes in two types: **Curved/Lateral Surface Area (CSA/LSA)** covers only the curved or side surfaces; **Total Surface Area (TSA)** includes top and bottom as well.
- **Volume** measures the space occupied by a 3D object — think of it as the capacity to hold water or sand.
- For composite figures, break them into standard shapes, calculate separately, then add or subtract as needed.
- Units matter: area is in square units (cm², m²), volume is in cubic units (cm³, m³). 1 m² = 10,000 cm²; 1 m³ = 1,000,000 cm³.
- **π (pi)** is taken as 22/7 or 3.14 unless specified otherwise in the question.
- A **hemisphere** is half a sphere — its CSA excludes the flat circular base; TSA includes it.
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Formulas / Key Facts
### 2D Figures
| Figure | Perimeter | Area | |--------|-----------|------| | Rectangle (l × b) | 2(l + b) | l × b | | Square (side a) | 4a | a² | | Triangle (base b, height h) | sum of sides | (1/2) × b × h | | Equilateral Triangle (side a) | 3a | (√3/4) × a² | | Circle (radius r) | 2πr (circumference) | πr² | | Semicircle | πr + 2r | (1/2)πr² | | Parallelogram (base b, height h) | 2(a + b) | b × h | | Rhombus (diagonals d₁, d₂) | 4 × side | (1/2) × d₁ × d₂ | | Trapezium (parallel sides a, b; height h) | sum of sides | (1/2) × (a + b) × h |