Mensuration — SSC MTS Study Notes

Overview

Mensuration deals with measurement of geometric figures — both flat (2-D) and solid (3-D) shapes. In SSC MTS Paper 1, expect 2–4 direct questions testing formulas for area, perimeter, surface area, and volume. Most questions are straightforward formula substitution, though some involve unit conversion or composite figures.

This topic is a score-booster because formulas are fixed and calculation steps are mechanical. Master the 10–12 core formulas, practice unit conversions (cm to m, m² to cm²), and recognize when a problem involves combining multiple shapes. Accuracy in applying the correct formula and careful arithmetic are the keys to full marks.

Common question types: find the area of a triangle given base and height; calculate the cost of painting four walls of a room; determine how much water a cylindrical tank holds; find the diagonal of a rectangle or cuboid. Questions may be direct or wrapped in a one-step word problem.

Key Concepts

• **2-D figures** have only length and width — we measure their **perimeter** (boundary length) and **area** (surface covered). Common shapes: square, rectangle, triangle, circle, trapezium.

• **3-D solids** have length, width, and height — we measure **surface area** (total outer surface) and **volume** (space occupied). Common solids: cube, cuboid, cylinder, cone, sphere, hemisphere.

• **Perimeter** is always in linear units (cm, m) while **area** is in square units (cm², m²). **Volume** is in cubic units (cm³, m³, litres where 1 litre = 1000 cm³).

• **Composite figures**: Some problems combine shapes — e.g. a rectangle with a semicircle on top. Break the figure into known shapes, calculate separately, then add or subtract as needed.

• **Unit conversion**: 1 m = 100 cm, so 1 m² = 10,000 cm² and 1 m³ = 1,000,000 cm³. Always convert to the same unit before calculation.

• **Diagonal** formulas: For rectangle/cuboid, use Pythagoras theorem. Rectangle diagonal = √(l² + b²). Cuboid diagonal = √(l² + b² + h²).

• In **cost problems**, Total Cost = (Area or Volume) × Rate per unit. E.g., cost of flooring = floor area × rate per m².

Formulas / Key Facts

**2-D Figures:**

• **Rectangle**: Perimeter = 2(l + b); Area = l × b; Diagonal = √(l² + b²)

• **Square**: Perimeter = 4a; Area = a²; Diagonal = a√2 (where a = side)

• **Triangle**: Perimeter = a + b + c (sum of sides); Area = ½ × base × height. For equilateral triangle of side a: Area = (√3/4)a²

• **Circle**: Circumference = 2πr or πd; Area = πr² (where r = radius, d = diameter, π ≈ 22/7 or 3.14)

• **Semicircle**: Perimeter = πr + 2r (curved part + diameter); Area = (πr²)/2

• **Trapezium**: Area = ½ × (sum of parallel sides) × height = ½(a + b)h

• **Parallelogram**: Area = base × height