Maths formula for class 8

Mensuration Formula for class 8

Formulas are the basics of any chapter you learn. Understanding the formulas well is chapter half done. Math formula for class 8 provided here will help you to solve your problems more quickly and with accuracy. Understanding the concept of formulas will make the problem solving easy. Remembering the formula is quite difficult but not impossible. Here we come up with the list of all the Maths formulas used in class 8. So memorize these formulas and crack your problems more quickly.

Maths Formula for Class 8

Maths formula for class 8 can be divided into two parts Geometric formulas and algebraic formulas. Mastering these formulas help you to understand the logic behind the problem and make it easy to solve it.

All Maths formulas for class 8 will make the student more confident to solve any problem more quickly and easily. Practicing more and more problems will make you easy to use these formulas.

8-grade Math Formula Chart

Here is the chart of 8th grade Math formulas which will help you to visualize all the formulas at a glance. Memorizing these formulas will help you to solve the problems more quickly and with accuracy. Some important geometric and algebraic formulas are mentioned in the 8 grade Math formula chart below.

Here we have tried to cover all Maths formula of class 8 chapter wise which will be required to solve different problems.

Rational Number Formulas

Additive Identity

a + 0 = a

Multiplicative Identity

a x 1  = a

Multiplicative inverse

(a/b) x (b/a) = 1

Distributive Property

a(b+c) = ab+ac

a(b-c) = ab-ac

Commutative Property of Addition

a+b = b+a

Commutative Property of Subtraction

a-b ≠ b-a

Commutative Property of Multiplication

axb = bxa

Commutative Property of Division

a/b ≠ b/a

Associative Property of Addition

(a+b)+c = a+(b+c)

Associative Property of Subtraction

(a-b)-c ≠ a-(b-c)

Associative Property of Multiplication

(axb)xc = ax(bxc)

Associative Property of Division

(a/b)/c ≠ a/(b/c)

 

Mensuration Formulas


Geometric shapes are of two types 2D shapes and 3D shapes.

Let us cover the formulas for 2D shapes

Perimeter and Area of Some Geometrical Figures

  • Perimeter

The measurement of the boundary of a plane figure is known as its perimeter.

  • Area

The magnitude of measurement of a plane region enclosed by a simple closed figure is called its area.


S.No

Name

Abbreviations used

Perimeter in units of length

Area in Square units

1.

Rectangle

a= length,

b= breadth,

d =diagonal

P = 2( a+ b)

d =(a2 +  b2)

A = ab

2.

Square

a = side 

d = diagonal

P = 4a

d = √2a

A = a2 = 1/2 (diagonal)2

3.

Parallelogram

a= side

b= side adjacent to a

h = height


P = 2(a+b)

A = ah

4.

Rhombus

a  = side

d1d2 = two diagonals

P = 4a

a= (d1/2)2+(d2/2)2 

A =½ d1d2 


5.

Quadrilateral

AC = diagonals

h1 , h2= altitudes

P = Sum of its four sides

A = ½ (AC)(h1+h2)

6.

Trapezium

a, b = parallel sides 

h = distance between the parallel sides

P = Sum of all sides

A= ½ h ( a+b)

7.

Triangle

a, b, c = sides 

b = base

h = altitude

P = a+ b + c

A = ½ b x h

8.

Right triangle

b = base

h = height

d= hypotenuse

P= b + h + d

A= ½ b x h

9.

Equilateral triangle

a = side

h = altitude

P= 3a

A = ½ a x h

10.

Isosceles triangle

a = equal sides

c = unequal sides

P = 2a +c

A = c √(4 a2-c2)/4 

11.

Isosceles right triangle

d = hypotenuse

a = equal sides

P = 2a + d

A = ½ a2

12.

Circle 

r = radius

π = 22/7


P=2 π r

A =πr2

13.

Semicircle

r = radius

P = π r + 2r

A =½ πr2

14.

Ring 

R= outer radius

r = inner radius

………………..

A = π(R2 - r2)


Area and volume related to 3d shapes(Solid shapes)


S.No

Name 

Abbreviations used

Lateral /curved surface area

Total surface area

Volume

1.

Cuboid

H=height, l is length and b is breadth

2h(l+b)

6l2

L*b*h

2.

Cube

a = length of the sides

4a2

6a2

a3

3.

Right Prism

..

Perimeter of Base × Height

Lateral Surface Area + 2(Area of One End)

Area of Base × Height

4.

Right Circular Cylinder

r= radius

h=height

2 (π × r × h)

2πr (r + h)

πr2h

5.

Right pyramid

..

½ (Perimeter of Base × Slant Height)

Lateral Surface Area + Area of the Base

⅓ (Area of the Base) × Height

6.

Right Circular Cone

r = radius

l = length

πrl

πr (l + r)

⅓ (πr2h)

7.

Sphere

r = radius

4πr2

4πr2

4/3πr3

8. 

Hemisphere

r = radius

2πr2

3πr2

⅔ (πr3)


Algebra Formula for class 8

1.  (a + b)2 = a2 + 2ab +b2

2.  (a - b)2= a2 - 2ab + b2

3.  (a + b)(a - b)= a2 - b2

4.  (x + a)(x + b)= x2 +(a - b)x + ab

5. (x + a)(x - b)= x2 + (a - b)x - ab

6 .(x - a)(x + b)= x2 + (b - a)x - ab

7. (x - a)(x - b)= x2 - (a + b)x + ab

8. (a - b)3 = a3 - b3- 3ab( a - b)

9. (a + b)3 = a3 + b3+ 3ab( a+ b)


Comparing Quantities Formulas


Selling Price(S.P) = Cost Price(C.P) + Profit(P)

Profit(P) = Selling Price(S.P) – Cost Price(C.P)

Loss(L) = Cost Price(C.P) – Selling Price(S.P)

Profit(P)% = Profit/C.P x 100%

Loss% = Loss/C.P x 100%

Simple Interest(S.I) = (P x R x T)/100

Compound Interest(C.I) = P(1+R/100)n

Where P is Principal Interest

            R is rate of Interest

            T is Time

             n is duration


Exponents and Powers Formulas

pm x pn = pm+n

{pm}⁄{pn} = pm-n

(pm)n = pmn

p-m = 1/pm

p1 = p

P0 = 1


Solved examples:

Example 1:

Find the volume and surface area of a cuboid of l= 10cm, b = 8cm and h = 6 cm.

Solution: We have Volume of cuboid = V = l x b x h 

    =10 x 8 x 6

      = 480cm2

Surface area = 2 ( lb + lh + bh)

= 2( 10x8 + 10x6 + 8x6)

=2(80 + 60 + 48)

=376cm2

Quiz:

Solve

1.Find the area of the right-angled triangle whose base is 12cm and hypotenuse 13cm.

Ans. 30cm2

2. Find the side of a cube whose surface area is 600cm2.

Ans. 10cm


FAQ (Frequently Asked Questions)

1. What is Mensuration in Maths?

Everywhere around us there are different 2D and 3D shapes. The branch of mathematics that deals with measurements of different 2D and 3D geometrical shapes. Mensuration formulas are used to measure the length, width, areas, volume, etc. of the different shapes like triangle, circle, sphere, cone, etc.

2. Why do we study mensuration?

The Study of mensuration helps us in calculating different measurements of the 2d and 3d shapes. Mensuration is used in day to day life. Some of the examples are:

  • Measurement of fields, for building a house.

  • Measurement of volume of a can, to carry milk.

  • Measurement of the surface area of the walls for estimation of painting it.

  • Measurements of the volume of food for packaging.