Mensuration
Area, Surface Area and Volume of Solids
---
Overview
Mensuration is the branch of mathematics dealing with the measurement of geometric figures—their lengths, areas and volumes. For JKTET Paper II, this topic bridges arithmetic computation with spatial reasoning, testing whether candidates can apply formulas to real-world and exam-style problems involving two-dimensional shapes and three-dimensional solids.
This topic carries significant weight because questions are straightforward once formulas are memorised, yet careless errors in unit conversion or formula selection cause avoidable mark loss. Mastery requires knowing the standard formulas for plane figures (triangles, quadrilaterals, circles) and solids (cuboid, cube, cylinder, cone, sphere), understanding when to use lateral versus total surface area, and being comfortable converting between cm², m², cm³ and litres.
Expect 2–4 direct application questions in the mathematics section. Speed and accuracy here can boost your score reliably.
---
Key Concepts
- **Area** measures the extent of a two-dimensional surface; 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; for solids with a base and top, distinguish between **lateral (curved) surface area** (LSA/CSA) and **total surface area** (TSA).
- **Volume** measures the space enclosed by a three-dimensional object; expressed in cubic units (cm³, m³) or litres (1 litre = 1000 cm³).
- For composite figures, break them into standard shapes, compute individually, then add or subtract as required.
- Unit consistency is critical: convert all measurements to the same unit before substituting into formulas.
- The value of π is typically taken as 22/7 or 3.14 unless otherwise specified.
---
Formulas / Key Facts
### Plane Figures (Area and Perimeter)
| Figure | Area | Perimeter | |--------|------|-----------| | Rectangle | l × b | 2(l + b) | | Square | a² | 4a | | Triangle (general) | ½ × base × height | sum of three sides | | Right triangle | ½ × base × height | a + b + hypotenuse | | Equilateral triangle | (√3/4) × a² | 3a | | Parallelogram | base × height | 2(a + b) | | Rhombus | ½ × d₁ × d₂ | 4a | | Trapezium | ½ × (sum of parallel sides) × height | sum of all sides | | Circle | πr² | 2πr (circumference) | | Semicircle | ½ πr² | πr + 2r |
### Three-Dimensional Solids