**Maths Formulas **are created by expert teachers from latest edition books. Basic Maths formulas enables students to complete the syllabus in a unique do-learn-do pattern of study. These mathematical formulas helps 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
- Math Formulas are indispensable for students preparing for competitive Exams and Board Exams.
- Math formula empower students for hands-on practice and help them to score high both in-class exams and boards.

## Maths Formulas | Class 6 to Class 12

### Important Maths Formulas | Area Formulas

- Area of a Circle Formula = π r
^{2}

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 =
*a*^{2} - 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 the bases of it. - 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 \(A =\frac{1}{2} r^{2}\left(\frac{\pi}{180} \theta-\sin \theta\right) \) - 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 r

### Algebra Formulas | Maths Formulas

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

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

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 x^{2} = 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 **fraction** ?

Fraction is 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 part 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 query regarding Class 6 to Class 12 Maths Formulas, drop a comment below and we will get back to you at the earliest.

### FAQs on 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.