Mensuration
Area, Surface Area and Volume of 2D and 3D Figures
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Overview
Mensuration is the branch of mathematics dealing with the measurement of geometric figures — their lengths, areas, and volumes. For GTET Paper-2, this topic carries significant weightage in the Mathematics section and tests your ability to apply formulas accurately to solve practical problems involving 2D shapes (plane figures) and 3D shapes (solid figures).
The syllabus expects you to calculate areas and perimeters of standard 2D figures like triangles, quadrilaterals, and circles, as well as surface areas and volumes of 3D solids such as cubes, cuboids, cylinders, cones, and spheres. Questions typically involve direct formula application, word problems requiring conversion of units, and composite figures combining multiple shapes.
Mastery of this topic requires memorising key formulas, understanding when to apply each, and being careful with unit conversions. Many exam questions test whether candidates can distinguish between surface area (paint needed to cover a solid) and volume (capacity or space occupied).
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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 2D figure, expressed in linear units (cm, m).
- **Surface Area** of a 3D solid is the total area of all its outer faces — Curved Surface Area (CSA) excludes bases, while Total Surface Area (TSA) includes all surfaces.
- **Volume** measures the space occupied by a 3D solid, expressed in cubic units (cm³, m³, litres where 1 litre = 1000 cm³).
- **Composite figures** are shapes formed by combining two or more basic shapes — solve by adding or subtracting individual areas/volumes.
- **Unit conversion** is critical: 1 m = 100 cm, 1 m² = 10000 cm², 1 m³ = 1000000 cm³ = 1000 litres.
- **Relationship between diameter and radius**: d = 2r; always check which is given in the problem.
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Formulas / Key Facts
### 2D Figures — Area and Perimeter
| Figure | Area | Perimeter | |--------|------|-----------| | Rectangle | l × b | 2(l + b) | | Square | a² | 4a | | Triangle | ½ × base × height | Sum of all 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 | 4a | | Trapezium | ½ × (a + b) × h | Sum of all sides | | Circle | πr² | 2πr (circumference) | | Semicircle | ½ × πr² | πr + 2r |