List of formulae

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Algebraic Identities

  • (a+b)(a-b)=a^2-b^2
  • (a+b)^2=a^2+2ab+b^2
  • (a-b)^2=a^2-2ab+b^2
  • (x+a)(x+b)=x^2+x(a+b)+ab
  • (x+a)(x+b)(x+c)=x^3+x^2(a+b+c)+x(ab+bc+ca)+abc
  • (a+b)^3=a^3+3ab(a+b)+b^3
  • (a-b)^3=a^3-3ab(a-b)-b^3
  • a^3+b^3=(a+b)(a^2-ab+b^2)
  • a^3-b^3=(a-b)(a^2+ab+b^2)
  • (a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca
  • a^4+a^2b^2+b^4=(a^2+b^2+ab)(a^2+b^2-ab)
  • (a+b+c)^3-a^3-b^3-c^3=3(a+b)(b+c)(c+a)
  • (a+b)(b+c)(c+a)=(a+b+c)(ab+bc+ca)-abc


Geometric Results

Formulae for commercial arithmetic

Statistical Formulae

Mensuration

Area and Perimeter of Plane Figures

Name Perimeter Area
Triangle (a+b+c), where a, b, c are sides \frac{1}{2}bh

where "h" is the height from any vertex to the opposite side "b"

Circle 2{\pi}r {\pi}r^2
Square 4a

Where a is the side of a square

a^2
Rectangle 2(l+b)

Where l & b are the length & breadth

lb
Trapezium (a+b+c+d)

Where a,b,c and d are the sides

\frac{1}{2}h(a+b)

Where a and b are parallel sides of trapezium. And h is the perpendicular distance between two parallel sides.

Parallelogram 2(a+b)

Where a & b are the sides of Parallelogram

bh

Where b is base and h is the perpendicular distance between base b and its parallel side.

Rhombus 4a

Where a is the side of a rhombus

\frac{1}{2}(d_{1}d_{2})

Where d1 and d2 are diagonals of rhombus

LSA(CSA) TSA & VOLUME of Solid Figures

Name of the Solid LSA(CSA)in sq.units TSA in sq.units VOLUME in cubic units
CUBE 4l^2

Where lenght(l)=breadth(b)=height(h)

6l^2 l^3
CUBOID 2h(l+b) 2(lb+bh+lh) lbh
PRISM

1)EQUILATERAL TRIANGLE RIGHT PRISM

Ph

Where P=3a is the perimeter of base triangle

2B+Ph

Where B=\frac{\sqrt{3}a^2}{4} is the area of base

Bh

Where B=\frac{\sqrt{3}a^2}{4}

2)SQUARE BASED RIGHT PRISM Ph

Where P=4a is the perimeter of base square

2B+Ph

Where B=a^2 is the area of base

Bh

Where B=a^2

PYRAMID

1)EQUILATERAL TRIANGLE BASED RIGHT PYRAMID

\frac{1}{2}Pl

Where P=3a is the perimeter of base triangle
l is the slant height

B+\frac{1}{2}Pl

Where B=\frac{\sqrt{3}a^2}{4} is the area of base

\frac{1}{3}Bh

Where B=\frac{\sqrt{3}a^2}{4}

2)SQUARE BASED RIGHT PYRAMID \frac{1}{2}Pl

Where P=4a is the perimeter of base square
l is the slant height

B+\frac{1}{2}Pl

Where B=a^2 is the area of base

\frac{1}{3}Bh

Where B=a^2

CYLINDER 2{\pi}rh

Where r is the radius of circular base

2{\pi}r(r+h)

where "h" is the height of cylinder

{\pi}r^2h
CONE {\pi}rl

Where l is the slant height

{\pi}r(l+r)

Where r is the radius of circular base

\frac{1}{3}{\pi}r^2h

Where h is the height or depth of the cone

FRUSTUM OF CONE {\pi}(r_{1}+r_{2})l

Where l=\sqrt{h^2+(r_{1}-r_{2})^2}

Failed to parse (lexing error): π{{(r_{1}+r_{2})l+r_{1}^2+r_{2}^2}}

Where r_{1} & r_{2} are the radii of two bases(r_{1}>r_{2})

\frac{1}{3}{\pi}h(r_{1}^2+r_{2}^2+r_{1}r_{2})

Where h is the height or depth of the frustum ofcone

SPHERE 4{\pi}r^2 4{\pi}r^2 \frac{4}{3}{\pi}r^3
HEMISPHERE 2{\pi}r^2 3{\pi}r^2 \frac{2}{3}{\pi}r^3