Wednesday, 19 April 2017

Mensuration I- Introduction to Mensuration with a list of Mensuration Formulas For IBPS PO Exam

Problems on Mensuration are asked in IBPS PO and all other competitive exams which makes it a very important topic. Read on for an Introduction to Mensuration along a list of Mensuration Formulas.

mensuration formulas

Introduction to Mensuration is important to help you clear your basics and master this important topic for IBPS PO and Government Exams. We have all studied this topic in high school and know that it is a formula oriented topic. There are specific formulas for different parameters, we put the values in these Mensuration formulas and get the desired answers. But at the same time it is also a calculation heavy topic so it is crucial that you use smart methods for these calculations.
mensuration formulas

What is Mensuration?

Mensuration is a topic in Geometry which is a branch in mathematics. Mensuration deals with length, area and volume of different kinds of shape- both 2D and 3D. So moving ahead in 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). 
mensuration formula

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). 
mensuration formula

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

mensuration formulas


Rectangle: Mensuration Formulas

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Scalene Triangle: Mensuration Formulas

mensuration formulas


Equilateral Triangle: Mensuration Formulas

mensuration formulas


Isosceles Triangle: Mensuration Formulas

mensuration formulas

Right Angled Triangle: Mensuration Formulas

mensuration formulas

Circle: Mensuration Formulas

mensuration formulas


Cube: Mensuration Formulas

mensuration formulas

 

Cuboid: Mensuration Formulas

mensuration formulas

Sphere: Mensuration Formulas

mensuration formulas

Hemisphere: Mensuration Formulas

mensuration formula

Cylinder: Mensuration Formulas

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Cone: Mensuration Formulas

mensuration formulas

You should know his entire list of Mensuration Formulas by heart to be able to solve questions. Read the next post in this series where we discuss how to solve simple and complex problems on 2D shapes.

Till then- Don’t Stop Practicing!
mensuration formulas
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