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 cm^{2} = 100 mm^{2}
- 1 m^{2} = 10000 cm^{2}
- 1 hectare = 10000 m^{2}
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.
Comments
write a comment