Mensuration
Overview
Mensuration is the branch of mathematics concerned with the measurement of geometric figures—their lengths, areas, and volumes. For TN TET, this topic carries significant weightage in the Mathematics section and tests your ability to apply formulas to calculate perimeter, area, surface area, and volume of standard 2D and 3D shapes.
The scope covers figures that students encounter from Classes 1–8: rectangles, squares, triangles, circles, parallelograms, trapeziums, cubes, cuboids, cylinders, cones, and spheres. Questions typically involve direct formula application, unit conversion, or word problems requiring you to identify the correct shape and formula. Mastery here also supports the pedagogy section, as you must understand how to teach these concepts through concrete-pictorial-abstract progression.
Expect 3–5 questions on mensuration in Paper I and Paper II. Accuracy depends on memorising formulas correctly, handling units carefully, and visualising the figure described in word problems.
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Key Concepts
- **Perimeter** is the total length of the boundary of a 2D figure. Think of it as the length of fence needed to enclose a field.
- **Area** is the measure of the surface enclosed within a 2D boundary, expressed in square units (cm², m²).
- **Surface Area** of a 3D solid is the total area of all its outer faces. Lateral (curved) surface area excludes the base(s); Total surface area includes everything.
- **Volume** measures the space occupied by a 3D object, expressed in cubic units (cm³, m³, litres where 1 litre = 1000 cm³).
- **Unit Conversion** is critical: 1 m = 100 cm; 1 m² = 10,000 cm²; 1 m³ = 1,000,000 cm³ = 1000 litres.
- **π (pi)** is taken as 22/7 or 3.14 unless specified otherwise. Use 22/7 when dimensions are multiples of 7 for cleaner calculations.
- **Composite Figures**: Many problems combine shapes (e.g., a rectangle with a semicircular end). Break them into standard parts, calculate separately, then add or subtract.
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Formulas / Key Facts
### 2D Figures
| Figure | Perimeter | Area | |--------|-----------|------| | Square (side a) | 4a | a² | | Rectangle (l × b) | 2(l + b) | l × b | | Triangle (sides a, b, c; base b, height h) | a + b + c | ½ × b × h | | Equilateral Triangle (side a) | 3a | (√3/4) × a² | | Parallelogram (base b, height h, sides a, b) | 2(a + b) | b × h | | Rhombus (diagonals d₁, d₂; side a) | 4a | ½ × d₁ × d₂ | | Trapezium (parallel sides a, b; height h) | sum of all sides | ½ × (a + b) × h | | Circle (radius r) | 2πr (circumference) | πr² | | Semicircle (radius r) | πr + 2r | ½ × πr² |