Mensuration Formula of 2D and 3D Figures

Question

Let's know all about mensuration formula, perimeter and area for class 6, 7, 8, 9, 10 this will very helpful to understand the concept very well.

Answer 1

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
Mensuration formula for 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)
Mensuration formula for Equilateral Triangle		Perimeter= 3xSide Area = \(\frac{\sqrt{3}}{4}\) (side)2
Mensuration formula for Square		Perimeter: 4 x side Area: (side)2
Mensuration formula for Rectangle		Perimeter= 2(length + breadth) Area= length x breadth
Mensuration formula for Parallelogram		Perimeter= 2(1st side + 2nd side) Area= base x height
Mensuration formula for Rhombus		Perimeter= 4 x side Area= \(\frac{1}{2}\) D1 x D2
Mensuration formula for Trapezium		Perimeter= sum of all sides Area= \(\frac{1}{2}\) (sum of parallel sides)x altitude
Mensuration formula for Circle		Circumference= 2πr Area= πr2 (where r is radius)
Mensuration formula for Semicircle	semi circle	Perimeter= πr+2r Area=\(\frac{1}{2}\)πr2

Mensuration formula for 3-D figures:

3 D figures	Figures	Formula
Mensuration formula for Cuboid		Surface Area: 2(lb+bh+lh) Volume = L x B x H Diagonal = \(\sqrt{l^{2}+b^{2}+h^{2}}\)
Mensuration formula for Cube		Surface Area= 6 x (side)2 Volume = (side)3 Diagonal = \(\sqrt{3}\)a
Mensuration formula forRight prism		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
Mensuration formula for Right Circular cylinder		Lateral surface area = 2πrh Total surface area= 2πrh + 2πr2 Volume= πr2h
Mensuration formula for Pyramid		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
Mensuration formula for Sphere		Surface area= 4πr2 Volume= \(\frac{4}{3}\)πr3
Mensuration formula for Hemisphere		Lateral Surface area= 2πr2 Total surface area= 3πr2 Volume= \(\frac{2}{3}\)πr3
Mensuration formula for Right circular cone		Slant Height= l = \(\sqrt{r^{2}+h^{2}}\) Lateral surface area= πrl Total surface area = πrl + πr2 Volume= \(\frac{1}{3}\) πr2h
Mensuration formula for Frustum of a cone	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.