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Monday 16 January 2023

Maths Formulas | Class 6 to Class 12

1/16/2023 09:13:00 am 0



Important Maths Formulas | Area Formulas

      1. Area of a Circle Formula = π r2
        where
        r – radius of a circleArea of a CircleArea of a Circle Formula
      2. Area of a Triangle Formula A=12bh
        where
        b – base of a triangle.
        h – height of a triangle.
        Area of a Triangle
      3. Area of Equilateral Triangle Formula = 34s2
        where
        s is the length of any side of the triangle.
        Area of Equilateral Triangle Formula
      4. Area of Isosceles Triangle Formula = 12bh
        Area of Isosceles Triangle Formula
        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 = a2
        Area of a Square Formula
      6. Area of a Rectangle Formula = L. B
        where
        L  is the length.
        B is the Breadth.Area of a Rectangle Formula
      7. Area of a Pentagon Formula = 52s.a
        Where,
        s is the side of the pentagon.
        a is the apothem length.
        Area of a Pentagon Formula
      8. Area of a Hexagon Formula = 332x2
        where
        where “x” denotes the sides of the hexagon.
        Area of a Hexagon Formula
        Area of a Hexagon Formula = 32.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 = 2a2(1+2)
        Consider a regular octagon with each side “a” units.
        Area of an Octagon Formula
      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:
        Area of a Regular Polygon Formulawhere
        s  is the length of any side
        n  is the number of sides
        tan  is the tangent function calculated in degrees
        Area of Regular Polygon Formula
      11. Area of a Parallelogram Formula = b . a
        where
        b is the length of any base
        a is the corresponding altitude
        Area of Parrallelogram Formula
        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).
        Area of Rhombus Formula
      13. Area of a Trapezoid Formula = The number of square units it takes to completely fill a trapezoid.
        Formula: Average width × Altitude
        Area of a Trapezoid Formula
        The area of a trapezoid is given by the formula
        Area of Trapezoid Maths Formulaswhere
        b1, b2 are the lengths of each base
        h is the altitude (height)
        Area of a Trapezoid Maths Formulas
      14. Area of a Sector Formula (or) Area of a Sector of a Circle Formula =  πr2(C360)
        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
        Area of a Sector FormulaSector 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×r2(θsinθ)
        Area of a Segment in Degrees A=12r2(π180θsinθ)

        Area of a Segment of a Circle Formula
        Area of a Segment of a Circle Formula
      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.
        Area under the Curve Maths FormulasArea under the Curve Formula

Algebra Formulas | Maths Formulas

1. a2b2=(a+b)(ab)

2. (a+b)2=a2+2ab+b2

3. a2+b2=(ab)2+2ab

4. (ab)2=a22ab+b2

5. (a+b+c)2=a2+b2+c2+2ab+2ac+2bc

6. (abc)2=a2+b2+c22ab2ac+2bc

7. (a+b)3=a3+3a2b+3ab2+b3;(a+b)3=a3+b3+3ab(a+b)

8. (ab)3=a33a2b+3ab2b3

9. a3b3=(ab)(a2+ab+b2)

10. a3+b3=(a+b)(a2ab+b2)

11. (a+b)4=a4+4a3b+6a2b2+4ab3+b4

12. (ab)4=a44a3b+6a2b24ab3+b4

13. a4b4=(ab)(a+b)(a2+b2)

14. a5b5=(ab)(a4+a3b+a2b2+ab3+b4)

15. (x+y+z)2=x2+y2+z2+2xy+2yz+2xz

16. (x+yz)2=x2+y2+z2+2xy2yz2xz

17. (xy+z)2=x2+y2+z22xy2yz+2xz

18. (xyz)2=x2+y2+z22xy+2yz2xz

19. x3+y3+z33xyz=(x+y+z)(x2+y2+z2xyyzxz)

20. x2+y2=12[(x+y)2+(xy)2]

21. (x+a)(x+b)(x+c)=x3+(a+b+c)x2+(ab+bc+ca)x+abc

22. x3+y3=(x+y)(x2xy+y2)

23. x3y3=(xy)(x2+xy+y2)

24. x2+y2+z2xyyzzx=12[(xy)2+(yz)2+(zx)2]

25. if n is a natural number, anbn=(ab)(an1+an2b++bn2a+bn1)

26. if n is even n = 2k, an+bn=(a+b)(an1an2b++bn2abn1)

27. if n is odd n = 2k+1, an+bn=(a+b)(an1an2b+bn2a+bn1)

28. (a+b+c+)2=a2+b2+c2++2(ab+bc+)

29. =am+n

30. =1

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 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.


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