Maths Formulas

Important Maths Formulas | Area Formulas

• • 1. Area of a Circle Formula = π r ²
       where
       r – radius of a circle
    2. Area of a Triangle Formula A=\( \frac{1}{2} b h \)
       where
       b – base of a triangle.
       h – height of a triangle.
       
    3. Area of Equilateral Triangle Formula = \( \frac{\sqrt{3}}{4} s^{2} \)
       where
       s is the length of any side of the triangle.
       
    4. 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.
    5. Area of a Square Formula = a ²
       
    6. Area of a Rectangle Formula = L. B
       where
       L is the length.
       B is the Breadth.
    7. Area of a Pentagon Formula = \( \frac{5}{2} s . a \)
       Where,
       s is the side of the pentagon.
       a is the apothem length.
       
    8. 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.
    9. Area of an Octagon Formula = \( 2 a^{2}(1+\sqrt{2}) \)
       Consider a regular octagon with each side “ a” units.
       
    10. 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
        
    11. Area of a Parallelogram Formula = b . a
        where
        b is the length of any base
        a is the corresponding altitude

        

        Area of Parallelogram: The number of square units it takes to completely fill a parallelogram.
        Formula: Base × Altitude
    12. Area of a Rhombus Formula = b . a
        where
        b is the length of the base
        a is the altitude (height).
        
    13. 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)
        
    14. 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.
    15. 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 \(A =\frac{1}{2} r^{2}\left(\frac{\pi}{180} \theta-\sin \theta\right) \)

        

    16. 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.
        

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.