Mensuration
Overview
Mensuration is the branch of mathematics dealing with measurement of geometric figures — their lengths, areas and volumes. For Bihar TET Paper II, this topic carries significant weight as it tests both conceptual understanding and computational ability. Questions typically involve plane figures (2D shapes like triangles, quadrilaterals, circles) and solids (3D objects like cubes, cylinders, cones, spheres).
This topic bridges pure geometry with real-world applications — calculating land area, tank capacity, material required for construction. Upper-primary students encounter mensuration extensively in Classes 6–8, so TET aspirants must master not just the formulas but also the pedagogical approach to teach these concepts effectively. Expect 3–5 direct questions requiring formula application, unit conversion and multi-step problem solving.
Success demands memorising key formulas, understanding when to apply each, and avoiding common unit-conversion errors. The exam favours questions combining two or more concepts — for example, finding the cost of painting a room (surface area) or the time to fill a tank (volume and rate).
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Key Concepts
- **Perimeter** is the total length of the boundary of a plane figure; measured in linear units (cm, m).
- **Area** measures the region enclosed by a plane figure; measured in square units (cm², m²).
- **Surface area** of a solid is the total area of all its outer faces; includes lateral (curved) surface area and total surface area.
- **Volume** measures the space occupied by a solid; measured in cubic units (cm³, m³) or capacity units (litres, where 1 litre = 1000 cm³).
- **Lateral Surface Area (LSA)** excludes the base and top; **Total Surface Area (TSA)** includes all surfaces.
- **Right prisms and cylinders** have uniform cross-section; their volume = Base Area × Height.
- **Pyramids and cones** have volume equal to one-third of the corresponding prism/cylinder with same base and height.
- **Unit conversion** is critical: 1 m = 100 cm; 1 m² = 10000 cm²; 1 m³ = 1000000 cm³ = 1000 litres.
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Formulas / Key Facts
### Plane Figures (2D)
| Figure | Perimeter | Area | |--------|-----------|------| | Rectangle | 2(l + b) | l × b | | Square | 4a | a² | | Triangle | a + b + c | ½ × base × height | | Right Triangle | a + b + c | ½ × leg₁ × leg₂ | | Equilateral Triangle | 3a | (√3/4) × a² | | Parallelogram | 2(a + b) | base × height | | Rhombus | 4a | ½ × d₁ × d₂ | | Trapezium | sum of all sides | ½ × (a + b) × h, where a, b are parallel sides | | Circle | 2πr (circumference) | πr² | | Semicircle | πr + 2r | ½ × πr² |