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Chapter 5-Mensuration

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


Mensuration is the process of measuring anything. The universe we exist in is three-dimensional. In both elementary and high school algebra, the principle of calculation is crucial. Furthermore, mensuration has a substantial impact on our daily lives. We learn to weigh objects in both 3D and 2D as we learn to measure them. Mensuration is a branch of mathematics concerned with calculating 2D and 3D figures based on parameters such as duration, volume, form, and surface area.

Volume, perimeter and area are important topics of mathematics seen in daily life. It holds true for every shape or scale, whether regular or irregular.

  • Area
    The region bounded by an object’s form is known as its area. The area of a shape is the space occupied by a figure or other geometric object. Their proportions and properties determine the shapes’ area. Different shapes have different measurement areas. The area of a square is not the same as the area of a kite.
  • Perimeter
    The total distance around a form is known as its perimeter. In a nutshell, it’s the duration of every shape as extended linearly. Based on the lengths, the perimeters of various forms will be the same length.
  • Volume
    The volume of an entity or material is the sum of space it takes up, estimated in cubic units. Two-dimensional objects have little volume and do have surface space.

The area of a flat form or surface of an entity may be described in geometry as its space. The amount of unit squares that cover the surface of a closed figure is the figure’s area. Square centimetres, square feet, square inches, and other similar units are used to quantify area.

The area of a rectangle in a two-dimensional plane is the area occupied by the rectangle. A rectangle is a two-dimensional (two-dimensional) structure with four sides and four vertices. The rectangle’s four angles are both right angles. The rectangle’s opposite sides are identical and parallel to one another.

Rectangle Area = Length x Breadth

We consider the length of a square’s side when calculating its area. A square’s area is proportional to the sum on its faces, so its area is equivalent to its sides’ square.

Area of a Square = Side × Side

When solving several problems, it is essential to convert units. Mathematical conversions are needed to complete the calculations. E.g., if a base is in centimetres and a height is in meters, and you have to find the area of a triangle in centimetres, you’ll need to translate the height in meters to centimetres. As a result, learning how to convert units is mandatory to convert a unit into the desired unit.

The situation determines a unit’s usage; for example, a room’s area is measured in meters, but a pencil’s length and thickness are measured in centimetres and millimetres, respectively.

As a result, we must convert one unit to another.

  • Cube: A cube is a three-dimensional object with the XYZ plane as its definition. There are six faces, eight vertices, and twelve edges on this object. Many of the cube’s faces are circular and have the same proportions.
  • Cuboid: A polyhedron with six faces, eight vertices, and twelve edges is known as a cuboid. The cuboid’s faces are parallel. However, not all of a cuboid’s faces are the same size.

Two essential and basic mathematical concepts are perimeter and area. They aid in quantifying physical space and laying the groundwork for more complex mathematics such as arithmetic, trigonometry, and calculus. Perimeter is a statistic of the width around a circle. Thus, the area indicates how much surface area the shape occupies.

People like architects, mechanics, and graphic designers use area and perimeter knowledge regularly, and it is a kind of math that is useful to the general public. When you paint a room, purchase a house, remodel a kitchen, or create a deck, knowing how much space you have and understanding how to put shapes together precisely can come in handy.

In this chapter, we learned about the basics of mensuration. We learned about some basic terms like perimeter, area, and volume.

  1. What role does mensuration play in our everyday lives?
    Mensuration is directly helpful in people’s vital practices. Agricultural zones, floor areas, or site areas must be measured for purchase/sale transactions.
  2. What is the meaning of the term “mensuration”?
    Measurement theory is the study of how things are measured. It is a division of mathematics concerned with the calculation of different geometric parameters.
  3. What is the difference between 2D and 3D mensuration?
    A 2D form is one enclosed by three or more straight lines in a plane. A 3D form is one surrounded by several surfaces or planes.
  4. What are the two mensuration systems?
    The metric (or decimal) method and the US standard system are the two most popular measurement units in the world. There are various units for calculating items like volume and mass in each system.
  5. What is a unit, and what are the different kinds of units?
    The unit is the measurement assigned for physical quantities. The fundamental quantities are length, mass, time, temperature, luminous strength, and electric current.

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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
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