Mensuration Formulas for Class 6 to 10

Mensuration formulas list contains all important mensuration formulas for Class 6 to 10.

By Mohit ChauhanPublished : Aug 11, 2020 , 16:46 IST
Mensuration Formulas for Class 6 to 10

Learning mensuration formulas is a challenging task, especially for students who hate Maths. In every class, you will find a complete chapter based on finding the area and perimeter of close plane figures. To define mensuration, it is a branch of geometry in which you need to measure geometrical figures and their parameters, which are as follows.

  • Length or breadth
  • Area
  • Perimeter
  • Volume
  • Lateral surface area
  • Curved surface area
  • Total surface area, etc. 

You will come across mensuration formulas of various 2-D and 3-D figures such as square, rectangle, triangle, circle, cuboid, cube, cylinder, sphere, cone, and hemisphere. In this article, you can view mensuration formulas for Classes 6 to 10. Before studying the formulas of mensuration, it is important to understand a few important terminologies related to mensuration. 

Important Terms of Mensuration

To understand and implement geometry in day-to-day applications, you must have a thorough understanding of the important definition of mensuration. We have tabulated the terms and their meanings below. 

Terms

Definitions

Closed Figures

In geometry, a closed figure is defined as an enclosed shape in which all its line segments or curves are connected with each other. 

Area

The region occupied by a two-dimensional close figure is called its area. 

Perimeter

It is the total length of a closed figure along the boundary.

Circumference

It is the total distance covered when you move around the circular path once along the boundary. 

Surface Area

It is the sum of the areas of faces of a solid figure. 

Volume

The region occupied by a three-dimensional solid figure is called its volume. 

Frustum of a Cone

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

Mensuration Formulas for Class 6

In NCERT Class 6 Maths textbook, you will study the following formulas of mensuration. 

Figure

Area

Perimeter

Rectangle

Length x Breadth

2 (length + breadth)

Square

Side x Side 

4 x length of its side 

Equilateral Triangle

½ x Base x Height

3 x length of a side

Mensuration Formulas for Class 7

Apart from the three basic mensuration formulas, two additional formulas will come to use when you solve questions of Class 7 Maths NCERT book. Also, go through the common conversions which are given below the table. 

Figure

Area

Perimeter

Rectangle

length x breadth

2 (length + breadth)

Square

side x side 

4 x length of its side 

Equilateral Triangle

½ x base x height

3 x length of a side

Parallelogram

base x height

Total distance along the boundary

Circle

𝛑r2

2𝛑r

Conversions

  • 1 cm2 = 100 mm2
  • 1 m2 = 10000 cm2
  • 1 hectare = 10000 m2

Mensuration Formulas for Class 8

In Class 8, you will study the area and perimeter of trapezium and rhombus. Further, in the mensuration chapter of NCERT Class 8 Maths, you will learn to calculate the total surface area, curved surface area, and volume of closed figures. 

Figure

Area

Perimeter

Trapezium

½ x (sum of the length of the parallel sides) x distance between the parallel sides)

Total distance along the boundary

Rhombus

½ x product of its diagonals

Total distance along the boundary

Total Surface Area, Curved Surface Area and Volume of Closed Figures

Here you can learn to calculate the TSA, LSA/CSA, and volume of closed figures such as cuboid, cylinder, and cube. Also learn the basic conversions that will help you solve NCERT Maths textbook questions easily. 

Figure

Total Surface Area

Lateral/Curved Surface Area

Volume

Cuboid

2 (lb + bh + hl)

2(l + b) x h

l x b x h

Cube

6 x (length)2

4 x (length)2

(length)3

Cylinder

2πr (r + h)

2πrh

πr2h

Conversions

  • 1 cm3 = 1 ml
  • 1 L = 1000 cm3
  • 1 m3 = 1000000 cm3 = 1000 L

Mensuration Formulas for Class 9

In Class 9, you will learn to calculate the TSA, CSA/LSA, and volume of a cone, sphere, and hemisphere. 

Figure

Total Surface Area

Lateral/Curved Surface Area

Volume

Cuboid

2 (lb + bh + hl)

2(l + b) x h

l x b x h

Cube

6 x (length)2

4 x (length)2

(length)3

Cylinder

2πr (r + h)

2πrh

πr2h

Cone

πr (l + r)

πrl

1/3πr2

Sphere

4πr2

-

4/3πr3

Hemisphere

3πr2

2πr2

2/3πr3

Mensuration Formulas for Class 10

The formulae involving the frustum of a cone are as follows.

1. Total surface area of a frustum of a cone = πl (r1 + r2) + π(r12 + r22)

where, h = vertical height of the frustum, l = slant height of the frustum

r1 and r2 are radii of the two bases of the frustum

2. Curved surface area of a frustum of a cone = πl (r1 + r2), where l = √h2 + (r1 - r2)2

3. Volume of a frustum of a cone = 1/3 πh (r12 + r22 + r1r2)

These were all mensuration formulas that you will cover in NCERT textbooks of Classes 6 to 10. You can apply these formulas in a variety of questions related to geometry or revolving around such shapes.

Frequently Asked Questions

  • How to remember mensuration formulas?

    Do not try to learn the formulas instead you should understand the derivation of each formula. Also, by breaking a figure into different shapes can help you derive the formula.

  • What is the formula of trapezium?

    Area of Trapezium= ½ x (sum of the length of the parallel sides) x distance between the parallel sides)

  • What is the total surface area of cylinder?

    Total Surface Area of Cylinder = 2πr (r + h)

  • What is the curved surface area of cone?

    Curved Surface Area of Cone = πrl

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