Mensuration
Area, Surface Area and Volume of Solids
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Overview
Mensuration is the branch of mathematics dealing with measurement of geometric figures — their lengths, areas and volumes. For CG TET Paper II, this topic carries significant weight as it tests both conceptual understanding and computational accuracy. Questions typically involve finding areas of plane figures, surface areas of 3D solids and volumes of common shapes.
This topic connects directly to real-life applications that teachers must convey to students: calculating land area, paint required for walls, water capacity of tanks, etc. Exam questions range from direct formula application to multi-step problems combining two or more shapes. Mastery requires memorising formulas accurately and knowing when to apply each.
The scope covers plane figures (triangles, quadrilaterals, circles) and solids (cube, cuboid, cylinder, cone, sphere). Understanding the difference between lateral surface area, total surface area and volume is essential for scoring full marks in this section.
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Key Concepts
- **Area** measures the region enclosed by a 2D 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 3D solid is the total area of all its outer faces — divided into Curved/Lateral Surface Area (CSA/LSA) and Total Surface Area (TSA).
- **Volume** measures the space occupied by a 3D object, expressed in cubic units (cm³, m³, litres where 1 litre = 1000 cm³).
- **Lateral Surface Area** excludes the base(s), while **Total Surface Area** includes all faces including base(s).
- **Right solids** have their axis perpendicular to the base — all formulas in the syllabus assume right solids unless stated otherwise.
- **Composite figures** combine two or more basic shapes — solve by adding or subtracting individual areas/volumes.
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Formulas / Key Facts
### Plane Figures (Area and Perimeter)
| Figure | Area | Perimeter | |--------|------|-----------| | Rectangle | l × b | 2(l + b) | | Square | a² | 4a | | Triangle | ½ × base × height | Sum of three sides | | Right Triangle | ½ × base × perpendicular | a + b + c | | Equilateral Triangle | (√3/4) × a² | 3a | | Parallelogram | base × height | 2(a + b) | | Rhombus | ½ × d₁ × d₂ | 4 × side | | Trapezium | ½ × (sum of parallel sides) × height | Sum of all sides | | Circle | πr² | 2πr (circumference) | | Semicircle | ½πr² | πr + 2r |
**Heron's Formula** for triangle with sides a, b, c: