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	1/3πr2h
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.