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Mensuration Formulas Class 10

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Last updated date: 25th Feb 2024
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An Introduction to Mensuration

Mensuration is a division of mathematics. In Mensuration, we study figures of geometry and its parameters such as length, slant length, area, height, volume, lateral surface area, surface area, etc. It is based on the principles of calculation and all the important equations and properties of different geometric shapes and figures.


Mensuration falls under the category of a subject of geometry. Mensuration deals with the size, region, and density of different forms, both two dimensions, and three dimensions. In this article, we will learn about Mensuration Formulas Class 10; we will know the concepts of mensuration that are detailed explained here with all the important mensuration formulas and properties of different geometric shapes and figures.

Important Parameters of Menurations

Some of the important parameters of Mensuration are given below.

  • Area:

The area is defined as the surface occupied by a defined closed region. It is often represented by the letter A and expressed in a square unit.

  • Perimeter (P):

The total length of the boundary of a region or a figure is referred to as its perimeter. Perimeter is measured only for two-dimensional shapes or figures. A continuous line along the edge of the closed vessel is the perimeter. It is given by the letter P, and measures are taken in a square unit.

  • Volume (V):

Volume is measured for any three-dimensional object. It can be defined as the quantity of three-dimensional space enclosed by a closed surface. Volume is given by the alphabet V, and the SI unit of measurement of volume is the cubic meter.

  • Curved Surface Area (CSA):

This is measured for the only cured surfaces. It is the area of the surface that is curved in the object, ignoring the other areas of the object that is not curved. CSA, an abbreviation, is used for the curved surface area.

  • Lateral Surface Area (LSA):

The total area of all the lateral surfaces of a given figure is called known as the Lateral Surface Area. These are the layers covering the artifact. The acronym used for convenience for the lateral surface area is LSA.

  • Total Surface Area (TSA):

The calculation of the total area of all surfaces of an object is called the Cumulative Surface Region in a closed shape. For example, we can calculate the total surface area of a cuboid by summation of the areas of all six surfaces. The acronym TSA is used for the total surface area.


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In Mensuration Chapter Class 10 a lot of basic formulas are introduced to students in this chapter. The formulas of the most basic two-dimensional and three-dimensional shapes are included in this class. In two-dimensional shapes, area and parameters are measured. A list of Formulas of Mensuration Class 10 for two dimensions figures are given below.


Mensuration Formulas List

S.No.

Name of Shape

Area

Perimeter (or Circumference)

1

Circle

\[ \pi(radius)^{2}\]

\[ 2 \pi \times radius \]

2

Square

\[side \times side\]

\[ 4 \times side\]

3

Rectangle

\[ Length \times Breadth\]

2(length + breadth)

4

Triangle

\[\frac{1}{2} \times height \times base\]

side1+ side2 + side3

5

Parallelogram

\[base \times height\]

2(length + breadth)

6

Rhombus

\[\frac{1}{2} \times first diagonal \times second diagonal \]

\[4 \times side\]


7

Trapezium

\[\frac{1}{2} \times height (base1 + base2)\]

base1 + base2 + side1 + side2



In a three dimensional object, we can calculate total surface area, curved surface area and volume. A list of Formulas of Mensuration Class 10 for three dimensions figures is given below.


S.No.

Shape Name

Total Surface Area

Lateral Surface Area

or

Curved Surface Area

Volume

1


Cube

\[6(side)^{2}\]

\[4(side)^{2}\]

\[(side)^{3}\]

2

Cuboid

\[2 (lenghth \times breadth + breadth \times height + height \times length) \]

\[2 \times height(length + breadth)\]

\[ Length \times breadth \times height\]


3

Cone

\[ \pi \times radius (radius + slant height) l\]

\[ \pi \times radius \times slant height\]

\[\frac{1}{3} \times \pi(radius)^{2} \times height\]

4

Cylinder

\[ 2 \pi \times radius \times height + 2 \pi(radius)^{2}\]

\[ 2 \pi \times radius \times height\]

\[\pi(radius)^{2} \times height\]

5

Sphere

\[4 \pi(radius)^{2}\]

\[4 \pi(radius)^{2}\]

\[\frac{4}{3} \times \pi(radius)^{3}\]

6


Hemisphere

\[3 \pi(radius)^{2}\]

\[2 \pi(radius)^{2}\]

\[\frac{2}{3} \times \pi(radius)^{3}\]


Example of Mensuration

Example-1: Calculate the perimeter of a park of rectangular shape with length 40 cm and breadth 80 cm.

Solution: First of all, let’s write all the given parameters.

Length of the rectangular park = 40 cm

Breadth of the rectangular park = 80cm

The perimeter of a rectangle= 2 (Lenght+Breadth)

=2 (40 + 80) cm

= 2(120) cm

= 240 cm

Hence the perimeter of the rectangular park is 240 cm


Example-2: Rakesh stays in a cuboidal room of dimensions 23x 12x 7. Calculate the total surface area of the room.

Solution: First of all, let’s write all the given parameters in the problem.

Length of the room= 23cm

Breadth of the room= 12 cm

Height of the room= 7cm

Total surface area of a cuboid= 2 (Lenght Breadth + BreadthHeight + LengthHeight)

= 2 (23×12 + 12×7 + 23×7)

= 2 (276 + 84 + 161)

= 2 (521)

= 1042 square cm


Do You Know?

  • When from the top of a right circular cone a small conical portion is removed, the solid we get is called a Frustum of a cone.


Hence Mensuration is an important concept of mathematics. We deal with the formula of mensuration in our normal life. The list of formulas is important for Mensuration Problems for Class 10. Students should always remember these basic formulas as they are important from the aspects of their examinations.

Competitive Exams after 12th Science

FAQs on Mensuration Formulas Class 10

1. What is mensuration?

The simplest definition of mensuration is that it is an act of measuring. Mensuration deals with the measurement of different types of geometric figures and their parameters such as length, volume, shape, surface area, lateral surface area, etc. In our daily life, we deal with such calculations. The formulas for two dimension and three dimension shapes are different because their parameters of measurement are different. In geometry, we are encountered with such problems where we need to calculate these parameters.

2. What has been included in CBSE Class 10 Mathematics Mensuration?

In Mensuration, we perform measurement of geometric figures on their parameters such as breadth, height, length, volume, surface area, lateral surface area, etc. The students of class 10 are introduced to the basic formulas for the measurement of these parameters. These formulas mainly include the calculations of the volume and surface area of standard two-dimensional and three-dimensional. Students can apply the formulas of mensuration in a variety of Mensuration Problems For Class 10  related to the geometry of such shapes.

3. What is the difference between two-dimensional and three-dimensional mensuration?

Two-dimensional mensuration basically deals with the calculations on perimeter and area. The shape that is two-dimensional is triangle, square, rectangle, circle, parallelogram, etc. The total length of the boundary of a shape is referred to as the perimeter, and the region enclosed by the figure is called the area. These shapes have no height or depth. The three-dimensional shape is defined as any shape that is surrounded by a number of surfaces or planes. The three-dimensional shapes are also known as solid shapes, and unlike two-dimensional shapes, they have both height and depth. We know that we can perform measurement on the area and perimeter of 2D shapes while in a three-dimensional shape we do the measurement of the volume, CSA, LSA, or TSA of shapes.