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Important Maths Formulas | Area Formulas

• • 1. Area of a Circle Formula = π r2
       where
       r – radius of a circle
    2. Area of a Triangle Formula A=12bh
       where
       b – base of a triangle.
       h – height of a triangle.
       
    3. Area of Equilateral Triangle Formula = 3√4s2
       where
       s is the length of any side of the triangle.
       
    4. Area of Isosceles Triangle Formula = 12bh
       
       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
       
    6. Area of a Rectangle Formula = L. B
       where
       L  is the length.
       B is the Breadth.
    7. Area of a Pentagon Formula = 52s.a
       Where,
       s is the side of the pentagon.
       a is the apothem length.
       
    8. Area of a Hexagon Formula = 33√2x2
       where
       where “x” denotes the sides of the hexagon.
       
       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.
       
    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 =  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
        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×r2(θ−sinθ)
        Area of a Segment in Degrees A=12r2(π180θ−sinθ)

        

    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. a2−b2=(a+b)(a−b)

2. (a+b)2=a2+2ab+b2

3. a2+b2=(a−b)2+2ab

4. (a−b)2=a2−2ab+b2

5. (a+b+c)2=a2+b2+c2+2ab+2ac+2bc

6. (a−b−c)2=a2+b2+c2−2ab−2ac+2bc

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

8. (a−b)3=a3−3a2b+3ab2−b3

9. a3−b3=(a−b)(a2+ab+b2)

10. a3+b3=(a+b)(a2−ab+b2)

11. (a+b)4=a4+4a3b+6a2b2+4ab3+b4

12. (a−b)4=a4−4a3b+6a2b2−4ab3+b4

13. a4−b4=(a−b)(a+b)(a2+b2)

14. a5−b5=(a−b)(a4+a3b+a2b2+ab3+b4)

15. (x+y+z)2=x2+y2+z2+2xy+2yz+2xz

16. (x+y−z)2=x2+y2+z2+2xy−2yz−2xz

17. (x−y+z)2=x2+y2+z2−2xy−2yz+2xz

18. (x−y−z)2=x2+y2+z2−2xy+2yz−2xz

19. x3+y3+z3−3xyz=(x+y+z)(x2+y2+z2−xy−yz−xz)

20. x2+y2=12[(x+y)2+(x−y)2]

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

22. x3+y3=(x+y)(x2−xy+y2)

23. x3−y3=(x−y)(x2+xy+y2)

24. x2+y2+z2−xy−yz−zx=12[(x−y)2+(y−z)2+(z−x)2]

25. if n is a natural number, an−bn=(a−b)(an−1+an−2b+…+bn−2a+bn−1)

26. if n is even n = 2k, an+bn=(a+b)(an−1−an−2b+…+bn−2a−bn−1)

27. if n is odd n = 2k+1, an+bn=(a+b)(an−1−an−2b+…−bn−2a+bn−1)

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.

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