# Chapter 5-Mensuration

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

Introduction

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.

#### Introduction of Volume Perimeter 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.

#### Concept of Area

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.

#### Area of a Rectangle and a Square

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

#### Conversion of Units

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.

#### Cubes and Cuboids

• 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.

#### Concept of Perimeter and Introduction to Area

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.

#### Conclusion

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

#### FAQs

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
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• Electrons and Photons
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• Force And Laws Of Motion
• Gravitation
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• 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
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• The d-block and f-block elements
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### High School Biology

• Absorption and Movement of Water in Plants
• Anatomy of Flowering Plants
• Animal Kingdom
• Bacteria and Fungi-Friends and Foe
• Biodiversity and Conservation
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• Biological Classification
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• Biotechnology and its Applications
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• Breathing and Exchange of Gases
• Cell – Unit of Life
• Cell Cycle and Cell Division
• Cell Division and Structure of Chromosomes
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• Circulation
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• Diversity In Living Organisms
• Ecosystem
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• Excretory Products and their Elimination
• Flowering Plants
• Genes and Chromosomes
• Health and Diseases
• Health and Its Significance
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• Heredity and Variation
• How Do Organisms Reproduce?
• Human Diseases
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• Improvement In Food Resources
• Integumentary System- Skin
• Kingdom Fungi
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• 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
• 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 – 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
• 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
• 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
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• 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

• 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