Mensuration
Area, Surface Area and Volume of Solids
---
Overview
Mensuration is the branch of mathematics dealing with measurement of geometric figures—their lengths, areas and volumes. For Assam TET Paper II, this topic carries significant weightage as it tests both conceptual understanding and computational accuracy. Questions typically involve calculating areas of plane figures, surface areas of solids, and volumes of three-dimensional objects.
Mastery of mensuration requires memorizing key formulas and understanding when to apply each. The topic connects directly to real-life applications—calculating land area, capacity of tanks, material needed for construction—making it relevant for teaching upper primary students. Expect 2-4 questions combining direct formula application with word problems requiring unit conversion and multi-step reasoning.
---
Key Concepts
- **Area** measures the surface enclosed by a plane figure, expressed in square units (cm², m²).
- **Perimeter** is the total length of the boundary of a plane figure, expressed in linear units (cm, m).
- **Surface area** of a solid is the total area of all its outer faces—distinguish between curved surface area (CSA) and total surface area (TSA).
- **Volume** measures the space occupied by a solid, expressed in cubic units (cm³, m³); 1 litre = 1000 cm³.
- **Lateral surface area** refers to the area of the sides only, excluding top and bottom bases.
- **Right solids** have their axis perpendicular to the base—all TET formulas assume right solids unless stated otherwise.
- **Composite figures** require breaking down into simpler shapes, calculating separately, then adding or subtracting as needed.
---
Formulas / Key Facts
### Plane Figures (Area and Perimeter)
| Figure | Area | Perimeter | |--------|------|-----------| | Rectangle | l × b | 2(l + b) | | Square | a² | 4a | | Triangle | (1/2) × base × height | Sum of three sides | | Equilateral Triangle | (√3/4) × a² | 3a | | Parallelogram | base × height | 2(a + b) | | Rhombus | (1/2) × d₁ × d₂ | 4a | | Trapezium | (1/2) × (a + b) × h | Sum of all sides | | Circle | πr² | 2πr (circumference) | | Semicircle | (1/2)πr² | πr + 2r |
### Three-Dimensional Solids
| Solid | CSA / LSA | TSA | Volume | |-------|-----------|-----|--------| | Cube (side a) | 4a² | 6a² | a³ | | Cuboid (l, b, h) | 2h(l + b) | 2(lb + bh + hl) | l × b × h | | Cylinder (r, h) | 2πrh | 2πr(r + h) | πr²h | | Cone (r, h, l) | πrl | πr(r + l) | (1/3)πr²h | | Sphere (r) | 4πr² | 4πr² | (4/3)πr³ | | Hemisphere (r) | 2πr² | 3πr² | (2/3)πr³ |