Mensuration

Overview

Mensuration is the branch of mathematics that deals with the measurement of geometric figures—their lengths, areas, and volumes. For HP TET, this topic carries significant weight as it tests both conceptual understanding and computational accuracy. Questions typically involve two-dimensional figures (perimeter and area) and three-dimensional solids (surface area and volume).

As a teacher candidate, you must not only solve these problems but also understand how to teach measurement concepts to young learners. The topic connects abstract formulas to real-world applications—calculating land area, paint needed for walls, or water capacity of tanks. Mastery here demonstrates your ability to make mathematics practical and meaningful.

Expect 3–5 questions from mensuration covering basic shapes at the primary level and extending to composite figures for TGT. Focus on memorising standard formulas and practising unit conversions, as careless errors in these areas cost easy marks.

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Key Concepts

• **Perimeter** is the total length of the boundary of a closed figure. Think of it as the length of fence needed to enclose a plot.

• **Area** measures the surface enclosed within a boundary, expressed in square units (cm², m²). It answers "how much space does this cover?"

• **Surface area** extends the concept of area to three-dimensional objects—the total area of all faces/surfaces of a solid.

• **Volume** measures the space occupied by a three-dimensional object, expressed in cubic units (cm³, m³, litres). It answers "how much can this hold?"

• **Lateral/Curved Surface Area** refers to the area of the sides only, excluding the top and bottom bases.

• **Unit consistency** is critical: all measurements must be in the same unit before applying any formula. Convert cm to m or vice versa as needed.

• **Composite figures** are shapes formed by combining two or more basic shapes. Break them into simpler parts, calculate separately, then add or subtract.

• **π (pi)** is approximated as 22/7 or 3.14 for calculations involving circles, cylinders, cones, and spheres.

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Formulas / Key Facts

### Two-Dimensional Figures

| Figure | Perimeter | Area | |--------|-----------|------| | Square (side a) | 4a | a² | | Rectangle (l × b) | 2(l + b) | l × b | | Triangle (sides a, b, c; base b, height h) | a + b + c | ½ × b × h | | Equilateral Triangle (side a) | 3a | (√3/4) × a² | | Circle (radius r) | 2πr (circumference) | πr² | | Semicircle (radius r) | πr + 2r | ½ × πr² | | Parallelogram (base b, height h) | 2(a + b) | b × h | | Rhombus (diagonals d₁, d₂) | 4 × side | ½ × d₁ × d₂ | | Trapezium (parallel sides a, b; height h) | sum of all sides | ½ × (a + b) × h |