Mensuration Formulas PDF

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Mensuration Formulas

Hello friends, here we are going to present the Mensuration Formulas PDF for all of you. Mensuration is the branch of mathematics which deals with the study of different geometrical shapes, their areas and volumes in the broadest sense, it is all about the process of measurement.

To help the students who prepare for this chapter we have given the important details and information related to Mensuration Formulas pdf. Through the preparation, students can make one of the toughest chapters easy to learn. Here in this article, We have curated mensuration of many formulas listed for you.

Check out the Mensuration formulas for 2D,3D shapes and much more which can be very beneficial for you to understand this chapter. Here, the concepts of mensuration are explained and all the important mensuration formulas are provided which can be very useful for you.

Mensuration Formulas PDF / Mensuration Formulas for 2D Shapes 

The major 2D figures are square, triangle, rectangle, circle, rhombus and parallelograms. Let us now have a look at the mensuration formulas of all the important 2D geometrical figures:

Shapes	Area(A)	Perimeter(P)	Diagonal(d)	Nomenclature
Square	a2	4a	√2a	Side = a
Rectangle	l x b	2(l+b)	√2 (l2+b2)	Length = lBreadth = b
Rhombus	½ × d1 × d2	4a	2A/d2	Diagonals = d1 and d2
Parallelogram	p x h	2(p+q)	√(p2+q2-2pqcosβ)	Base = pSide = qAngle = β
Circle	πr2 (πr2)/2 (for semi-circle)	2πr R(π+2 (for semi-circle)	–	Radius = r

 3D Figures Mensuration Formulas

Below is a compilation of mensuration formulas for all the important 3D geometrical figures:

Shapes	Volume	Curved Surface Area/Lateral Surface Area	Total Surface Area	Nomenclature
N/A	4/3 πr3	4 πr2	4πr2	Radius = r
N/A	a3	4 x a2	6a2	Side = a
N/A	l x b x h	2h(l+b)	2(lb+bh+hl)	Length = l Breadth = b height = h
N/A	πr2 x h	2πrh	2πr(r+h)	Radius of base = r
N/A	1/3πr2h	πrl	πr(s+l)	Slant height = s
N/A	4/6 πr3	3πr2	2πr2	Radius = r

Difference Between 2D & 3D Shapes

Before diving it mensuration formulas, it is important to understand the two major types of geometric shapes, that is Two-dimensional (2D) and three-dimensional (3D).

2D Shapes	3D Shapes
A 2D shape refers to a figure which is surrounded by three or multiple straight lines in a plane.	A 3D shape is a figure covered by multiple surfaces or planes.
2D shapes do not contain any depth or height.	3D shapes are solid shapes and have depth as well as height.
They comprise 2D length and breadth.	They consist of length, breadth and width as they are three-dimension.
Area and perimeter of these shapes are measured.	Volume, CSA, LSA and TSA is measured for these shapes.

Mensuration Formulas: Important Terms

Before we get down to the nitty-gritty of the mensuration formulas, let us recall some important terms:

Term	Meaning	SI Units
Area (A)	It is the surface enclosed by a given shape.	m2 or cm2
Perimeter (P)	It is simply the boundary length of an area.	m or cm
Volume (V)	The space occupied by a solid or a 3-Dimensional object is called volume.	cm3 or m3
Curved Surface Area (CSA)	It is the area enclosed by the curved portion of a geometrical object.	m2 or cm2
Total Surface Area (TSA)	The sum total of areas of all the surfaces of an object is called TSA.	m2/cm2
Lateral Surface Area (LSA)	Sum total of areas of all surfaces except the top and the base of an object is called LSA.	m2/cm2
Diagonal (d)	A line that joins two vertices of a geometrical figure is called a diagonal.

Mensuration Formulas: Solved Examples

Here are some important solved examples for you to help you understand the mensuration formulas better-

Q. Find the perimeter of a rectangular park with a length of 20 cm and a breadth of 40 cm.

Ans:

Length of the rectangular park = 20 cm
Breadth of the rectangular park =40cm
Perimeter of a rectangle= 2 (L+B)
=2 (20 + 40) cm
= 2(60) cm
= 120 cm
The perimeter of the rectangular park is 120 cm

Q. Rohit stays in a cuboidal hotel room with dimensions 21x 10x 8. Find the total surface area of the room.

Ans:

Length of the room= 21cm
Breadth of the room= 10 cm
Height of the room= 8cm
Total surface area of a cuboid= 2 (LB + BH + LH)
= 2 (21×10 + 10×8 + 21×8)
= 2 (210 + 80 + 168)
= 2 (458)
= 916 cubic cm

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