**NCERT Maths Formulas **are created by expert teachers from the latest edition books. Basic Maths formulas enable students to complete the syllabus in a unique do-learn-do pattern of study. These mathematical formulas help students:

- Improve Score in Board Exams and Entrance Examinations.
- Makes Complete Preparation easy on time.
- Helps you in making revision
- Mind Maps and Tables Helps you to Memories easily.
- Know their strengths and weaknesses in Mathematics formula
- NCERT Math Formulas are indispensable for students preparing for competitive Exams and Board Exams.
- Math formula empowers students for hands-on practice and helps them to score high on both in-class exams and boards.

## NCERT Maths Formulas | Class 6 to Class 12

## Important NCERT Maths Formulas | Area Formulas

- Area of a Circle Formula = π r2

where

r – radius of a circle - Area of a Triangle Formula A=( frac{1}{2} b h )

where

b – base of a triangle.

h – height of a triangle.

- Area of Equilateral Triangle Formula = ( frac{sqrt{3}}{4} s^{2} )

where

s is the length of any side of the triangle.

- Area of Isosceles Triangle Formula = ( frac{1}{2} b h )

where:

a be the measure of the equal sides of an isosceles triangle.

b be the base of the isosceles triangle.

h be the altitude of the isosceles triangle. - Area of a Square Formula =
*a2*

- Area of a Rectangle Formula = L. B

where

*L*is the length.

B is the Breadth. - Area of a Pentagon Formula = ( frac{5}{2} s . a )

Where

s is the side of the pentagon.

a is the apothem length.

- Area of a Hexagon Formula = (frac{3 sqrt{3}}{2} x^{2} )

where

where “**x**” denotes the sides of the hexagon.

Area of a Hexagon Formula = (frac{3}{2} . d . t )

Where “**t**” is the length of each side of the hexagon and “**d**” is the height of the hexagon when it is made to lie on one of its bases of. - Area of an Octagon Formula = ( 2 a^{2}(1+sqrt{2}) )

Consider a regular octagon with each side “*a”*units.

- Area of Regular Polygon Formula:

By definition, all sides of a regular polygon are equal in length. If you know the length of one of the sides, the area is given by the formula:

where

*s*is the length of any side

*n*is the number of sides

*tan*is the tangent function calculated in**degrees**

- Area of a Parallelogram Formula = b . a

where

*b*is the length of any base

*a*is the corresponding altitudeArea of Parallelogram: The number of square units it takes to completely fill a parallelogram.

Formula: Base × Altitude - Area of a Rhombus Formula = b . a

where

*b*is the length of the base

*a*is the altitude (height).

- Area of a Trapezoid Formula = The number of square units it takes to completely fill a trapezoid.

Formula: Average width × Altitude

The area of a trapezoid is given by the formula

where

b1, b2 are the lengths of each base

h is the altitude (height)

- Area of a Sector Formula (or) Area of a Sector of a Circle Formula = (pi r^{2}left(frac{C}{360}right) )

where:

C is the central angle in degrees

r is the radius of the circle of which the sector is part.

π is Pi, approximately 3.142

Sector Area – The number of square units it takes to exactly fill a sector of a circle. - Area of a Segment of a Circle Formula

Area of a Segment in Radians (A =1 / 2 times r^{2}(theta-sin theta) )

Area of a Segment in Degrees (A =frac{1}{2} r^{2}left(frac{pi}{180} theta-sin thetaright) )

Area of a Segment of a Circle Formula - Area under the Curve Formula:

The area under a curve between two points is found out by doing a definite integral between the two points. To find the area under the curve y = f(x) between x = a & x = b, integrate y = f(x) between the limits of a and b. This area can be calculated using integration with given limits.

- Area of a Circle Formula = π r2

## Algebra Formulas | NCERT Maths Formulas

1. (a^{2}-b^{2}=(a+b)(a-b)) [mathjax]

2. ((a+b)^{2}=a^{2}+2 a b+b^{2})

3. (a^{2}+b^{2}=(a-b)^{2}+2 a b)

4. ((a-b)^{2}=a^{2}-2 a b+b^{2})

5. ((a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2 a b+2 a c+2 b c)

6. ((a-b-c)^{2}=a^{2}+b^{2}+c^{2}-2 a b-2 a c+2 b c)

7. ((a+b)^{3}=a^{3}+3 a^{2} b+3 a b^{2}+b^{3} ;(a+b)^{3}=a^{3}+b^{3}+3 a b(a+b))

8. ((a-b)^{3}=a^{3}-3 a^{2} b+3 a b^{2}-b^{3})

9. (a^{3}-b^{3}=(a-b)left(a^{2}+a b+b^{2}right))

10. (a^{3}+b^{3}=(a+b)left(a^{2}-a b+b^{2}right))

11. ((a+b)^{4}=a^{4}+4 a^{3} b+6 a^{2} b^{2}+4 a b^{3}+b^{4})

12. ((a-b)^{4}=a^{4}-4 a^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4})

13. (a^{4}-b^{4}=(a-b)(a+b)left(a^{2}+b^{2}right))

14. (a^{5}-b^{5}=(a-b)left(a^{4}+a^{3} b+a^{2} b^{2}+a b^{3}+b^{4}right))

15. ((x+y+z)^{2}=x^{2}+y^{2}+z^{2}+2 x y+2 y z+2 x z)

16. ((x+y-z)^{2}=x^{2}+y^{2}+z^{2}+2 x y-2 y z-2 x z)

17. ((x-y+z)^{2}=x^{2}+y^{2}+z^{2}-2 x y-2 y z+2 x z)

18. ((x-y-z)^{2}=x^{2}+y^{2}+z^{2}-2 x y+2 y z-2 x z)

19. (x^{3}+y^{3}+z^{3}-3 x y z=(x+y+z)left(x^{2}+y^{2}+z^{2}-x y-y z-x zright))

20. (x^{2}+y^{2}=frac{1}{2}left[(x+y)^{2}+(x-y)^{2}right])

21. ((x+a)(x+b)(x+c)=x^{3}+(a+b+c) x^{2}+(a b+b c+c a) x+a b c)

22. (x^{3}+y^{3}=(x+y)left(x^{2}-x y+y^{2}right))

23. (x^{3}-y^{3}=(x-y)left(x^{2}+x y+y^{2}right))

24. (x^{2}+y^{2}+z^{2}-x y-y z-z x=frac{1}{2}left[(x-y)^{2}+(y-z)^{2}+(z-x)^{2}right])

25. if n is a natural number, (a^{n}-b^{n}=(a-b)left(a^{n-1}+a^{n-2} b+ldots+b^{n-2} a+b^{n-1}right))

26. if n is even n = 2k, (a^{n}+b^{n}=(a+b)left(a^{n-1}-a^{n-2} b+ldots+b^{n-2} a-b^{n-1}right))

27. if n is odd n = 2k+1, (a^{n}+b^{n}=(a+b)left(a^{n-1}-a^{n-2} b+ldots-b^{n-2} a+b^{n-1}right))

28. ((a+b+c+ldots)^{2}=a^{2}+b^{2}+c^{2}+ldots+2(a b+b c+ldots))

29. (begin{aligned}left(a^{m}right)left(a^{n}right) &=a^{m+n} \(a b)^{m} &=a^{m} b^{m} \left(a^{m}right)^{n} &=a^{m n} end{aligned})

30. (begin{aligned} a^{0} &=1 \ frac{a^{m}}{a^{n}} &=a^{m-n} \ a^{m} &=frac{1}{a^{-m}} \ a^{-m} &=frac{1}{a^{m}} end{aligned})

## Root Maths Formulas

**Square Root :**

If x2 = y then we say that square root of y is x and we write √y = x

So, √4 = 2, √9 = 3, √36 = 6

**Cube Root:**

The cube root of a given number x is the number whose cube is x.

we can say the cube root of x by 3√x

- √xy = √x * √y
- √x/y = √x / √y = √x / √y x √y / √y = √xy / y.

## Fractions Maths Formulas

What is a **fraction**?

Fraction is the name of part of a whole.

Let the fraction number is 1 / 8.

**Numerator**: Number of parts that you of the top number(1)

**Denominator**: It is the number of equal parts the whole is divided into the bottom number (8).

We hope the Maths Formulas for Class 6 to Class 12, help you. If you have any queries regarding Class 6 to Class 12 Maths Formulas, drop a comment below and we will get back to you at the earliest.

## FAQs on NCERT Maths Formulas

**1.** **What is the best way to memorize Math Formulas?**

The best way to remember math formulas to learn how to derive them. If you can derive them then there is no need to remember them.

**2.** **How to learn Mathematics Formulas?**

Don’t try to learn the formula try learning the logic behind the formula and intuition behind it.

**3.** **What is Math Formula?**

Generally, each kind of maths has a formula or multiple formulas that help you work out a particular thing, whether it’s geometry, statistics, measurements, etc.

**4.** **Is it necessary to know how does a math formula work?**

It is indeed necessary to understand and be able to solve equations, either if you want to work as a mathematician, or any other field using mathematics, or if you want to be a math teacher or a teacher in a field that uses math.

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