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Mensuration Formula of 2D and 3D Figures for Class 6th to 10th

Mensuration

Mensuration Formula:

At first, let us know about Mensuration. It is a branch of mathematics which deals with the measurement of several parameters such as length, breadth, perimeter, area and volume of 2-dimensional and 3-dimensional objects. Mensuration formula for class 6, 7, 8, 9, 10 contains data of lines and angles for measurement of several parameters. Generally, it is used for geometrical figures where there is a need to find out dimensions, perimeter, area, volume and several other physical quantities.

Perimeter: It is the path surrounding the object’s area. We can also say that the length of boundary of an object is its perimeter. It is simply the addition of length so it has no powered units. Simply its unit is in m (metre), cm (centimetre), km (kilo-metre) etc. Mensuration formula for perimeter is different for different figures.

Area: It is the surface occupied by the 2-dimensional body. We can also define the area as that surface of object in a plane closed within a boundary. Millions of lines in a plane coexist to form an area so Its unit is squared as we multiply length to lengths. Its units are cm2, m2, km2 etc. The mensuration formula for area is different for different geometrical bodies.

Volume: It is the space occupied by any three-dimensional body within its surface boundary. How much Space it occupies includes several dimensions such as length, breadth, height. So its unit is always expressed in cubic units as cm3, m3, km3etc.

List of all the necessary mensuration formula orderly:

2D figures Figures Formula
Triangle mensuration formula of triangle Perimeter= Sum of all sidesArea = 1/2 b x h

Area = \(\sqrt{s(s-a)(s-b)(s-c)}\)

a, b, c are sides of triangle.

Where s=\(\frac{a+b+c}{2}\)

Area=\(\frac{1}{2}\) (bxh)

Equilateral Triangle mensuration formula for equilateral triangle Perimeter= 3xSide

Area = \(\frac{\sqrt{3}}{4}\) (side)2

Square mensuration formula for square Perimeter: 4 x side

Area: (side)2

Rectangle mensuration formula for rectangle Perimeter= 2(length + breadth)

Area= length x breadth

Parallelogram mensuration formula for parallelogram Perimeter= 2(1st side + 2nd side)

Area= base x height

Rhombus rhombus mensuration Perimeter= 4 x side

Area= \(\frac{1}{2}\) D1 x D2

Trapezium mensuration formula for trapezium Perimeter= sum of all sides

Area= \(\frac{1}{2}\) (sum of parallel sides)x altitude

Circle mensuration formula for circle Circumference= 2πr

Area= πr2 (where r is radius)

Semicircle
formula related to semicircle
semi circle
Perimeter= πr+2r

Area=\(\frac{1}{2}\)πr2

Mensuration formula for 3-D figures:

3 D figures   Formula
Cuboid mensuration formula for cuboid Surface Area: 2(lb+bh+lh)

Volume = L x B x H

Diagonal = \(\sqrt{l^{2}+b^{2}+h^{2}}\)

Cube cube mensuration formula Surface Area= 6 x (side)2

Volume = (side)3

Diagonal = \(\sqrt{3}\)a

Right prism mensuration of right prism area volume Lateral or curved surface area = perimeter of base x height

Total surface area =  lateral surface area + 2(area of ends)

Volume= Area of base x Height

Right Circular cylinder right circular cone mensuration formula for Bank, SSC, CBSE class 6, 7, 8, 9, 10 Lateral surface area = 2πrh

Total surface area= 2πrh + 2πr2

Volume= πr2h

Pyramid mensuration pyramid formula for class 8 Lateral surface area= \(\frac{1}{2}\) perimeter of base x slant height

Total surface area= lateral surface area + area of base

Volume= \(\frac{1}{3}\) (area of base) x height

Sphere sphere formula for mensuration clasas 6 Surface area= 4πr2

Volume= \(\frac{4}{3}\)πr3

Hemisphere   Lateral Surface area= 2πr2

Total surface area= 3πr2

Volume= \(\frac{2}{3}\)πr3

Right circular
cone
Cone lateral and total surface area as well as volume Slant Height= l = \(\sqrt{r^{2}+h^{2}}\)

Lateral surface area= πrl

Total surface area = πrl + πr2

Volume= \(\frac{1}{3}\) πr2h

Frustum of a
cone
mensuration for frustum volume
formulas
Slant Height= l = \(\sqrt{{h}^{2}+ ({r}_1-{r}_2)^{2}}\)

Lateral surface area= πl(r1+r2)

Total surface area= πl(r1+r2) + πr12+ πr22

Volume= \(\frac{1}{3}\)πh(r12+r1r2+r22)

Mensuration formula for Bank, railway, SSC exam and for class 6th to 10th:

The list of formulas with well-defined images will help you to memorise it easily. The formula list will help you to solve the problems related to mensuration much easily. Basic formulas are for class 6, then a little more added in each section of class 7, class 8, class 9, class 10 and so on.

FAQ on Mensuration Formula:

  1.  What are mensuration formulas?
    Mensuration itself means To measure. In mathematics, these formulas help in a different kind of measurement of 2D, 3D figure such as its perimeter, lateral and total surface area, Volume. These formula ease the problem-solving way. 
  2. How to remember mensuration formulas?
    To remember mensuration formulas you must make application of each formula in different types of problems. The more you practice problems more you will learn. Here formulas with figures is given so that it will be easy for you to learn.
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