Syllabus covered in the MSVgo app

Download MSVgo app now!

Chapter 6 – Mensuration

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:


Mensuration means measuring geometric figures and their parameters like length, volume, shape, surface area, lateral surface area, etc. While studying a closed plane figure, you need to know its perimeter and area. The perimeter is the distance around its boundary, and its area is the region covered by it. For example, before fencing a garden, you must know the perimeter to check the length of the fence required. While, to know about the amount of land occupied by the garden, you must know the area of the garden.

We can find the area and perimeter of various plane figures such as triangles, rectangles, circles etc. and solid surfaces like a cube, cuboid, sphere, etc.

Draw an equilateral triangle of each side measuring 6 cm and named as ABC. If you had to stick colourful tape on the triangle’s boundary, how much longer will you require? To find this, you must know the perimeter of the triangle.

The perimeter of Triangle = Sum of all the sides (Isosceles and Scalene Triangle)


The perimeter of Triangle = 4 x side (Equilateral triangle)

For the above triangle having sides of 6 cm,

Perimeter of triangle ABC = 4 x 6

Perimeter = 24 cm

It means you will need 24 cm long tape.

Now, if you want to colour the triangle, you must know the area of the triangle.

Area of Triangle = ½ × b × h

Where b= Base of the triangle and h = height of the triangle

If for this triangle, height was 4 cm, then

Area of Triangle ABC = ½ × 6 × 4

Area of Triangle ABC = 12 cm

If you are moving in a circular path and want to know the distance covered by you to complete one round, you must find the circle’s perimeter.

Circumference of the circle = 2 π r

Where the value of π is 22/7 or 3.14 and r is the radius of the circle.

If I have a circle with a radius of 14 m, then

Circumference of the circle = 2 x 22/7 x 14

Circumference of the circle = 88 m

If you were given two medium-sized pizzas and one large size pizza and you were asked to compare which one has more quantity, how will you find it? You need to find the medium pizza area and the large pizza to compare which one is larger.

Area of circle = π r2

If the medium pizza radius was 14 cm and the large pizza was 28 cm, then.

Area of one medium pizza = 22/7 x (14)2 = 616 cm2

Area of two medium pizza = 2 x 616 = 1,232 cm2

Area of one large pizza = 22/7 x (28)2 = 2,464 cm2

This signifies that one large pizza is larger than two medium pizzas.

Solid surfaces or objects are those which have three dimensions. All six faces are squares and identical in a cube-like Rubik’s cube. All six faces are rectangular, and the opposite faces are identical. If there are three pairs of identical faces, such an object is called a cuboid, like a duster used in your class.

Area and Volume of Cube

If you have asked the painter to paint a cubical room’s walls and tell you the cost per unit area, how will you find how much money you need to pay him? You need to find the lateral surface area of the cubical room first.

Lateral surface area of cube = 4 a2

a = side

If side of cube measures 250 cm, then

Lateral surface area of room = 4 x (250)2

Lateral surface area of room = 2,50,000 cm2

If you need to paint a cubical box of side 8 cm, you need to consider its total surface area.

The total surface area of cube = 6 a2

So, Total surface area of cubical box = 6 x (8)2 = 384 cm2

To find the amount of water that can be filled inside the cubical container, you must find the volume of a cube,

The volume of cube = a3

For the above mentioned cube, volume will be = (8)3 = 512 cm3

If you have a cuboidal-shaped geometry box and the teacher asked you to colour the box, leaving its top and bottom, how much area will you colour? To find this, you need to find the lateral surface area of your cuboidal box.

Lateral Surface area of cuboid = 2h(l + b)

Where, h = height; l = length; b = base

If you have a cuboidal box and you need to cover it entirely with glitter paper, then how much glitter paper will you require? You can find that by calculating the total surface area of the cuboid.

Total Surface Area of Cuboid = 2 (lb +bh +hl)

If you have a cuboidal mould to set the chocolate, how much liquid chocolate do you need to fill in it? You can know that with the help of finding the volume of the cuboidal box.

Volume of cuboid = l × b × h

Mensuration is studying different parameters in the plane figures and solid surfaces with the area, perimeter, circumference and volume. For a polygon like a triangle, the area and perimeter of different triangle types can be found differently. For solid surfaces like cube and cuboid, you need to understand the question first to determine whether you need to find the lateral surface area or total surface area.

Q1. What is mensuration?

A1. It is the measurement of geometric figures and their parameters like length, volume, shape, surface area, lateral surface area, etc.

Q2. What do you mean by the surface area of the object?

A2. It is the total area covered by the surface of the solid or 3-dimensional object.

Q3. Is surface area similar to volume?

A3. No, the surface area is a two-dimensional quantity, while volume is a three-dimensional quantity.

Q4.  What is the use of mensuration in daily life?

A4. Uses of mensuration in daily life are:

  1. Amount of carpet required in a room
  2. Fencing for the garden
  3. Reading the roadmap
  4. The volume of soil needed to fill a ditch

Q5. What is the formula of lateral surface area for cube and cuboid?

A5. Lateral surface area of cube = 4 a2

Lateral Surface area of cuboid = 2h(l + b)

There is a lot that you have learned about the area, perimeter, and volume of the triangle, circle, cube, and cuboid. To know about plant life further, you can download the MSVgo app, which offers a large base of learning videos, quizzes, interactive games, and many more to the students till grade 12.

High School Physics

  • Alternating Current
  • Atoms
  • Communication Systems
  • Current Electricity
  • Dual nature of Radiation and Matter
  • Electric Charges and Fields
  • Electricity
  • Electromagnetic Induction
  • Electromagnetic Waves
  • Electron Beams and Radioactivity
  • Electrons and Photons
  • Electrostatic Potential and Capacitance
  • Fluid Pressure
  • Force and Acceleration
  • Force And Laws Of Motion
  • Gravitation
  • Internal Energy
  • Kinetic Theory
  • Law of motion
  • Light – Reflection And Refraction
  • Magnetic Effects Of Electric Current
  • Magnetism and Matter
  • Management Of Natural Resources
  • Mechanical properties of Fluids
  • Mechanical properties of Solids
  • Motion
  • Motion in a plane
  • Motion in a straight line
  • Moving Charges and Magnetism
  • Nuclear Energy
  • Nuclei
  • Oscillations
  • Our Environment
  • Paths of Heat
  • Physical world
  • Ray optics and optical instruments
  • Semiconductor Devices
  • Semiconductor Electronics: Materials, Devices and Simple Circuits
  • Simple Machines
  • Sound
  • Sources Of Energy
  • Specific and Latent Heats
  • Spherical Mirrors
  • Static Electricity
  • Systems of Particles and Rotational motion
  • Thermal properties of matter
  • Thermodynamics
  • Units and Measurement
  • Vectors, Scalar Quantities and Elementary Calculus
  • Wave Optics
  • Waves
  • Work, Power and Energy

High School Chemistry

  • Acids, Bases and Salts
  • Alcohols, Phenols and Ethers
  • Aldehydes, Ketones and Carboxylic Acids
  • Aliphatic and Aromatic Hydrocarbons
  • Alkyl and Aryl Halides
  • Amines
  • Analytical Chemistry 
  • Atomic Structure
  • Atoms And Molecules
  • Basic concepts of Chemistry
  • Biomolecules
  • Carbon And Its Compounds
  • Carboxylic acids and Acid Derivatives
  • Chemical Bonding and Molecular Structures
  • Chemical Energetics
  • Chemical Equilibria
  • Chemical Kinetics
  • Chemical Reactions And Equations
  • Chemical Reactions and Their Mechanisms
  • Chemistry in Everyday Life
  • Chemistry of p-Block elements
  • Chemistry of Transition and Inner Transition
  • Classification of Elements
  • Coordination Compounds
  • Cyanide, Isocyanide, Nitro compounds and Amines
  • Electrochemistry
  • Electrolysis
  • Elements, Compounds and Mixtures
  • Environmental Chemistry
  • Equilibrium
  • Ethers and Carbonyl compounds
  • Haloalkanes and Haloarenes
  • Hydrocarbons
  • Hydrogen
  • Ideal solutions
  • Introduction to Organic Chemistry
  • Ionic equilibria
  • Matter
  • Matter Around Us
  • Matter In Our Surroundings
  • Metallurgy
  • Metals And Non-Metals
  • Mole Concept and Stoichiometry
  • Natural Resources
  • Organic Chemistry – Basic Principles
  • Periodic Classification of Elements
  • Physical and Chemical Changes
  • Physical and Chemical Properties of Water
  • Polymers
  • Preparation, Properties and Uses of Compounds
  • Principles and Processes of Isolation of Elements
  • Redox Reactions
  • Relative Molecular Mass and Mole
  • States of Matter
  • Structure Of The Atom
  • Study of Compounds
  • Study of Gas Laws
  • Study of Representative Elements
  • Surface Chemistry
  • The d-block and f-block elements
  • The Gaseous State
  • The p-Block Elements
  • The Periodic Table
  • The s-Block Elements
  • The Solid State
  • Thermodynamics

High School Biology

  • Absorption and Movement of Water in Plants
  • Adolescent Issues
  • Anatomy of Flowering Plants
  • Animal Kingdom
  • Bacteria and Fungi-Friends and Foe
  • Biodiversity and Conservation
  • Biofertilizers
  • Biological Classification
  • Biomedical Engineering
  • Biomolecules
  • Biotechnology and its Applications
  • Biotic Community
  • Body Fluids and Circulation
  • Breathing and Exchange of Gases
  • Cell – Unit of Life
  • Cell Cycle and Cell Division
  • Cell Division and Structure of Chromosomes
  • Cell Reproduction
  • Cellular Respiration
  • Chemical Coordination and Integration
  • Circulation
  • Control And Coordination
  • Crop Improvement
  • Digestion and Absorption
  • Diversity In Living Organisms
  • Ecosystem
  • Environmental Issues
  • Excretory Products and their Elimination
  • Flowering Plants
  • Genes and Chromosomes
  • Health and Diseases
  • Health and Its Significance
  • Heredity And Evolution
  • Heredity and Variation
  • How Do Organisms Reproduce?
  • Human Diseases
  • Human Eye And Colourful World
  • Human Health and Disease
  • Human Population
  • Human Reproduction
  • Hygiene
  • Improvement In Food Resources
  • Integumentary System- Skin
  • Kingdom Fungi
  • Kingdom Monera
  • Kingdom Protista
  • Life Processes
  • Locomotion and Movement
  • Microbes in Human Welfare
  • Mineral Nutrition
  • Molecular Basis of Inheritance
  • Morphology of Flowering Plants
  • Neural Control And Coordination
  • Nutrition in Human Beings
  • Organism and Population
  • Photosynthesis
  • Photosynthesis in Higher Plants
  • Plant Growth and Development
  • Plant Kingdom
  • Pollination and Fertilization
  • Pollution; Sources and its effects
  • Principles of Inheritance and Variation
  • Reproduction and Development in Angiosperms
  • Reproduction in Organisms
  • Reproductive Health
  • Respiration in Human Beings
  • Respiration in Plants
  • Respiratory System
  • Sexual Reproduction in Flowering Plants
  • Strategies for Enhancement in Food Production
  • Structural Organisation in Animals
  • Structural Organisation of the Cell
  • The Endocrine System
  • The Fundamental Unit Of Life
  • The Living World
  • The Nervous System and Sense Organs
  • Tissues
  • Transpiration
  • Transport in Plants

High School Math

  • Algebra – Arithmatic Progressions
  • Algebra – Complex Numbers and Quadratic Equations
  • Algebra – Linear Inequalities
  • Algebra – Pair of Linear Equations in Two Variables
  • Algebra – Polynomials
  • Algebra – Principle of Mathematical Induction
  • Algebra – Quadratic Equations
  • Binomial Theorem
  • Calculus – Applications of Derivatives
  • Calculus – Applications of the Integrals
  • Calculus – Continuity and Differentiability
  • Calculus – Differential Equations
  • Calculus – Integrals
  • Geometry – Area
  • Geometry – Circles
  • Geometry – Conic Sections
  • Geometry – Constructions
  • Geometry – Introduction to Euclid’s Geometry
  • Geometry – Three-dimensional Geometry
  • Geometry – Lines and Angles
  • Geometry – Quadrilaterals
  • Geometry – Straight Lines
  • Geometry – Triangles
  • Linear Programming
  • Matrices and Determinants
  • Mensuration – Areas
  • Mensuration – Surface Areas and Volumes
  • Number Systems
  • Number Systems – Real Numbers
  • Permutations and Combinations
  • Probability
  • Sequence and Series
  • Sets and Functions
  • Statistics 
  • Trignometry – Height and Distance
  • Trignometry – Identities
  • Trignometry – Introduction

Middle School Science

  • Acids, Bases And Salts
  • Air and Its Constituents
  • Basic Biology
  • Body Movements
  • Carbon and Its Compounds
  • Cell – Structure And Functions
  • Changes Around Us
  • Chemical Effects Of Electric Current
  • Chemistry in Your Life
  • Coal And Petroleum
  • Combustion And Flame
  • Components Of Food
  • Conservation Of Plants And Animals
  • Crop Production And Management
  • Electric Current And Its Effects
  • Electricity And Circuits
  • Elements and Compounds
  • Fibre To Fabric
  • Food production and management
  • Force And Pressure
  • Forests: Our Lifeline
  • Friction
  • Fun With Magnets
  • Garbage In, Garbage Out
  • Getting To Know Plants
  • Health and Hygiene
  • Heat
  • Hydrogen
  • Life Processes: Nutrition in Animals and Plants
  • Light, Shadows And Reflections
  • Materials: Metals And Non-Metals
  • Matter and Its States
  • Metals and Non-metals
  • Micro Organisms: Friend And Foe
  • Motion And Measurement Of Distances
  • Motion And Time
  • Nutrition In Animals
  • Nutrition In Plants
  • Organization in Living Things
  • Our Environment
  • Physical And Chemical Changes
  • Pollution and conservation
  • Pollution Of Air And Water
  • Reaching The Age Of Adolescence
  • Reproduction In Animals
  • Reproduction In Plants
  • Respiration In Organisms
  • Rocks and Minerals
  • Separation Of Substances
  • Simple Machines
  • Soil
  • Some Natural Phenomena
  • Sorting Materials Into Groups
  • Sound
  • Stars And The Solar System
  • Structure of Atom
  • Synthetic Fibers And Plastics
  • The Living Organisms And Their Surroundings
  • Transfer of Heat
  • Transformation of Substances
  • Transportation In Animals And Plants
  • Universe
  • Waste-water Story
  • Water: A Precious Resource
  • Weather, Climate And Adaptations Of Animals To Climate
  • Winds, Storms And Cyclones

Middle School Math

  • Addition
  • Area and Its Boundary
  • Boxes and Sketches
  • Data Handling
  • Fun With Numbers
  • Heavy and Light
  • How Many
  • Long And Short
  • Mapping
  • Measurement
  • Money
  • Multiplication and Factors
  • Multiply and Divide
  • Numbers
  • Parts and Wholes
  • Pattern Recognition
  • Patterns
  • Play With Patterns
  • Rupees And Paise
  • Shapes And Angles
  • Shapes And Designs
  • Shapes and Space
  • Similarity
  • Smart Charts
  • Squares
  • Subtraction
  • Tables And Shares
  • Tenths and Hundredths
  • Time
Please switch to portrait mode
for the best experience.
Click to open Popup