Mensuration
Area, Surface Area and Volume of 2D and 3D Figures
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Overview
Mensuration is the branch of mathematics dealing with measurement of geometric figures — their lengths, areas and volumes. For TS TET Paper II (classes 6-8), this topic carries significant weightage in the Mathematics section and tests your ability to apply formulas correctly to practical problems.
The topic divides naturally into two parts: **2D figures** (plane figures where we calculate perimeter and area) and **3D figures** (solid shapes where we calculate surface area and volume). Exam questions typically present word problems requiring you to identify the correct formula, substitute values carefully and compute the answer. Many questions involve unit conversions or combine multiple shapes.
Mastery requires memorising all standard formulas and understanding when each applies. The pedagogy aspect may ask about activity-based methods for teaching mensuration concepts to upper primary students.
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Key Concepts
- **Perimeter** is the total length of the boundary of a 2D figure; **area** is the region enclosed within that boundary.
- **Surface area** of a 3D solid is the total area of all its outer faces — think of it as the amount of paper needed to wrap the object completely.
- **Volume** measures the space occupied by a 3D object — the capacity it can hold.
- **Lateral (curved) surface area** excludes the top and bottom faces; **total surface area** includes all faces.
- Units matter: area is always in square units (cm², m²), volume in cubic units (cm³, m³). Converting between units requires squaring or cubing the conversion factor.
- Composite figures are solved by breaking them into standard shapes, calculating separately, then adding or subtracting as needed.
- π (pi) is taken as 22/7 or 3.14 unless specified otherwise in the problem.
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Formulas / Key Facts
### 2D Figures — Perimeter and Area
| 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 × base × perpendicular | | 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 | | Circle | 2πr (circumference) | πr² | | Semicircle | πr + 2r | ½ × πr² |
*Here: l = length, b = breadth, a = side, r = radius, h = height, d₁ and d₂ = diagonals*
### 3D Figures — Surface Area and Volume