Subject : Mathematics
Topic : Mensuration
S no. Topic Elaboration
1 Introduction to Mensuration
2 2D Shapes
3 3D Shapes
4 Important Terms
5 Mensuration Formula
6 Real Life Application
7 Exercise
What is Mensuration?
Mensuration is a topic in Geometry which is a branch of mathematics. Mensuration deals with length, area and
volume of different kinds of shape- both 2D and 3D. So moving ahead in the introduction to Mensuration, let us
discuss what are 2D and 3D shapes and the difference between them.
What is a 2D Shape?
Moving ahead with our introduction to Mensuration let’s discuss what is a 2D shape. A 2D shape is a shape that
is bounded by three or more straight lines or a closed circular line in a plane. These shapes have no depth or
height; they have two dimensions- length and breadth and are therefore called 2D figures or shapes. For 2D
shapes, we measure area (A) and perimeter (P).
What is a 3D Shape?
The next step in introduction to Mensuration is finding out what is a 3D shape. A 3D shape is a shape that is
bounded by a number of surfaces or planes. These are also referred to as solid shapes. These shapes have height
or depth unlike 2D shapes; they have three dimensions- length, breadth and height/depth and are therefore
called 3D figures. 3D shapes are actually made up of a number of 2D shapes. Also, know as solid shapes, for
3D shapes we measure Volume (V), Curved Surface Area (CSA), Lateral Surface Area (LSA) and Total
Surface Area (TSA).
Introduction to Mensuration: Important Terms
Before we move ahead to the list of important mensuration formulas, we need to discuss some important terms
that constitutes these mensuration formulas.
Area (A) – The surface occupied by a given closed shape is called its area. It is represented by the alphabet A
and is measured in unit square- m2/ cm2.
Perimeter (P) – The length of the boundary of a figure is called its perimeter. In other words, it is the
continuous line along the periphery of the closed figure. It is represented by the alphabet P and is measures in
cm/ m.
Volume (V) – The space that is contained in a three-dimensional shape is called its volume. In other words, it is
actually the space that is enclosed in a 3D figure. It is represented by the alphabet V and is measured in cm3/
m3.
Curved Surface Area (CSA) – In solid shapes where there is a curved surface, like a sphere or cylinder, the
total area of these curved surfaces is the Curved Surface Area. . The acronym for this is CSA and it is measured
in m2 or cm2.
Lateral Surface Area (LSA) – The total area of all the lateral surfaces of a given figure is called its Lateral
Surface Area. Lateral Surfaces are those surfaces that surround the object. The acronym for this is LSA and it is
measured in m2 or cm2.
Total Surface Area (TSA) – The sum of the total area of all the surfaces in a closed shape is called its Total
Surface Area. For example, in a cuboid when we add the area of all the six surfaces we get its Total Surface
Area. The acronym for this is TSA and it is measured in m2 or cm2.
Square Unit (m2/ cm2) – One square unit is actually the area occupied by a square of side one unit. When we
measure the area of any surface we refer to this square of side one unit and how many such units can fit in the
given figure. It is expressed as m2 or cm2, depending on the unit in which the area is being measure.
Cube Unit (m3/ cm3) – One cubic unit is the volume occupied by a cube of side one unit. When we measure
the volume of any figure we actually refer to this cube of side one unit and how many such unit cubes can fit in
the given closed shape. It is written in m3 or cm3, depending on the unit that is being used to measure.
List of Mensuration Formulas
Now that our introduction to mensuration and the important terms is over let’s move to the mensuration
formulas since this is a formula based topic. Every 2D and 3D figure has a list of mensuration formulas that
establish a relationship amongst the different parameters. Let’s discuss the mensuration formulas of some
shapes.
Square: Mensuration Formulas
Rectangle: Mensuration Formulas
Scalene Triangle: Mensuration Formulas
Equilateral Triangle: Mensuration Formulas
Isosceles Triangle: Mensuration Formulas
Right Angled Triangle: Mensuration Formulas
Circle: Mensuration Formulas
Cube: Mensuration Formulas
Cuboid: Mensuration Formulas
Sphere: Mensuration Formulas
Hemisphere: Mensuration Formulas
Cylinder: Mensuration Formulas
Cone: Mensuration Formulas
APPLICATIONS:
Real life applications are many. Mensuration is directly useful in important activities that people do.
1. Measurement of agricultural fields, floor areas or site areas required for purchase/selling transactions.
2. Measurement of volumes required for packaging milk, liquids, solid edible food items or non-edible items.
3. Measurements of surface areas required for estimation of painting houses buildings etc..
4. Volumes and heights are useful in knowing water levels and amounts in river or lakes.
5. Construction of overhead tanks.
6. Optimum cost packaging sachets for milk etc like tetra packing.
7. Estimations.
Amount of paint required to cover a certain surface area
Amount of carpet required for a particular room
Fencing needed for the perimeter of a garden
Pavement tessellation of a pathway
Volume of soil needed to fill in a ditch
The distance around a circular race track
Travel and roadmap reading
Amount of fuel needed for a given journey
Gift wrapping
Finding capacities of containers, tanks etc.
Cooking:
In cooking, we use measurements for volume when following recipe books. Tools such as measuring
jugs may be used to determine volume. When making a cake for example, we may need tins of a
specific width and length for a particular recipe. We may also need to weigh out the dry ingredients
using a measuring scale.
Weather Forecast:
Before leaving the house, we may want to check the weather. The temperature measured using
thermometers will help us determine what we choose to wear to keep us warm or cool.
Trip:
When planning a car journey, we may look at a map to find out the quickest way to reach a particular
destination. The map allows us to compare the different distances. We may look at how to cut down the
number of miles we have to travel by taking short cuts.
The time we take to travel can now be calculated by dividing distance over the speed of our car.
Size:
If we knew the size of our waist, then it is safe to buy skirts online even though may not have tried it out
first.
Why Is Mensuration Useful?
Mensuration is often based on making use of a model or base object that serves as the standard for making the
calculations. From that point, advanced mathematics is employed to project measurements of length, width and
weight associated with like items. The end result is data that can help to make the best use of resources
available today while still planning responsibly for the future.
Summary
We have been able to find that mensuration is used in our daily lives.
Mensuration is used by different kinds of formulas for measurements of different objects.
We have explained different ways that mensuration has improved on our activities, mostly by saving time.
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