Difference between revisions of "List of formulae"

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<mm>[[List of formulae.mm|flash]]</mm>
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=Algebraic Identities=
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*<math>(a+b)(a-b)=a^2-b^2</math>
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*<math>(a+b)^2=a^2+2ab+b^2</math>
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*<math>(a-b)^2=a^2-2ab+b^2</math>
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*<math>(x+a)(x+b)=x^2+x(a+b)+ab</math>
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*<math>(x+a)(x+b)(x+c)=x^3+x^2(a+b+c)+x(ab+bc+ca)+abc</math>
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*<math>(a+b)^3=a^3+3ab(a+b)+b^3</math>
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*<math>(a-b)^3=a^3-3ab(a-b)-b^3</math>
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*<math>a^3+b^3=(a+b)(a^2-ab+b^2)</math>
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*<math>a^3-b^3=(a-b)(a^2+ab+b^2)</math>
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*<math>(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca</math>
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*<math>a^4+a^2b^2+b^4=(a^2+b^2+ab)(a^2+b^2-ab)</math>
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*<math>(a+b+c)^3-a^3-b^3-c^3=3(a+b)(b+c)(c+a)</math>
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*<math>(a+b)(b+c)(c+a)=(a+b+c)(ab+bc+ca)-abc</math><br>
  
  
=Algebraic Identities=
 
 
=Geometric Results=
 
=Geometric Results=
 +
 
=Formulae for commercial arithmetic=
 
=Formulae for commercial arithmetic=
 +
=Statistical Formulae=
 
=Mensuration=
 
=Mensuration=
 
==Area and Perimeter of Plane Figures==
 
==Area and Perimeter of Plane Figures==
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{|class="wikitable"
 
{|class="wikitable"
 
|-
 
|-
|Shape
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|Name
 
|Perimeter
 
|Perimeter
 
|Area
 
|Area
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|Triangle
 
|Triangle
 
|(a+b+c), where a, b, c are sides
 
|(a+b+c), where a, b, c are sides
|
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|<math>\frac{1}{2}bh</math>
<math>\frac{3}{4}*b*h</math>
 
 
where "h" is the height from any vertex to the opposite side "b"
 
where "h" is the height from any vertex to the opposite side "b"
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|-
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|Circle
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|<math>2{\pi}r</math>
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|<math>{\pi}r^2</math>
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|-
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|Square
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|<math>4a</math>
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Where a is the side of a square
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|<math>a^2</math>
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|-
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|Rectangle
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|<math>2(l+b)</math>
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Where l & b are the length & breadth 
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|<math>lb</math>
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|-
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|Trapezium
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|<math>(a+b+c+d)</math>
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Where a,b,c and d are the sides
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|<math>\frac{1}{2}h(a+b)</math>
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Where a and b are parallel sides of trapezium. And h is the perpendicular distance between two parallel sides.
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|-
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|Parallelogram
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|<math>2(a+b)</math>
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Where a & b are the sides of Parallelogram
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|<math>bh</math>
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Where  b is base and h is the perpendicular distance between base b and its parallel side.
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|-
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|Rhombus
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|<math>4a</math>
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Where a is the side of a rhombus
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|<math>\frac{1}{2}(d_{1}d_{2})</math>
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Where d1 and d2 are diagonals of rhombus
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|-
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|}
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 +
==LSA(CSA) TSA & VOLUME of Solid Figures==
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 +
{|class="wikitable"
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|-
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|Name of the Solid
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|LSA(CSA)in sq.units
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|TSA in sq.units
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|VOLUME in cubic units
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|-
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|CUBE
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|<math>4l^2</math>
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Where lenght(l)=breadth(b)=height(h)
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|<math>6l^2</math>
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|<math>l^3</math>
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|-
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|CUBOID
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|<math>2h(l+b)</math>
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|<math>2(lb+bh+lh)</math>
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|<math>lbh</math>
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|-
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|PRISM
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1)EQUILATERAL TRIANGLE RIGHT PRISM
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|<math>Ph</math>
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Where P=3a is the perimeter of base triangle
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|<math>2B+Ph</math>
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Where B=<math>\frac{\sqrt{3}a^2}{4}</math> is the area of base
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|<math>Bh</math>
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Where B=<math>\frac{\sqrt{3}a^2}{4}</math>
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|-
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|2)SQUARE BASED RIGHT PRISM
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|<math>Ph</math>
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Where P=4a is the perimeter of base square
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|<math>2B+Ph</math>
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Where B=<math>a^2</math> is the area of base
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|<math>Bh</math>
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Where B=<math>a^2</math>
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|-
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|PYRAMID
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1)EQUILATERAL TRIANGLE BASED RIGHT PYRAMID
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|<math>\frac{1}{2}Pl</math>
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Where P=3a is the perimeter of base triangle<br>
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l is the slant height
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|<math>B+\frac{1}{2}Pl</math>
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Where B=<math>\frac{\sqrt{3}a^2}{4}</math> is the area of base
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|<math>\frac{1}{3}Bh</math>
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Where B=<math>\frac{\sqrt{3}a^2}{4}</math>
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|-
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|2)SQUARE BASED RIGHT PYRAMID
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|<math>\frac{1}{2}Pl</math>
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Where P=4a is the perimeter of base square<br>
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l is the slant height
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|<math>B+\frac{1}{2}Pl</math>
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Where B=<math>a^2</math> is the area of base
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|<math>\frac{1}{3}Bh</math>
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Where B=<math>a^2</math>
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|-
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|CYLINDER
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|<math>2{\pi}rh</math>
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Where r is the radius of circular base
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|<math>2{\pi}r(r+h)</math>
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where "h" is the height of cylinder
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|<math>{\pi}r^2h</math>
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|-
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|CONE
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|<math>{\pi}rl</math>
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Where l is the slant height
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|<math>{\pi}r(l+r)</math>
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Where r is the radius of circular base
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|<math>\frac{1}{3}{\pi}r^2h</math>
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Where h is the height or depth of the cone
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|-
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|FRUSTUM OF CONE
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|<math>{\pi}(r_{1}+r_{2})l</math>
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Where l=<math>\sqrt{h^2+(r_{1}-r_{2})^2}</math>
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|<math>π{{(r_{1}+r_{2})l+r_{1}^2+r_{2}^2}}</math>
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Where <math>r_{1}</math> & <math>r_{2}</math> are the radii of two bases<math>(r_{1}>r_{2})</math>
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|<math>\frac{1}{3}{\pi}h(r_{1}^2+r_{2}^2+r_{1}r_{2})</math>
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Where h is the height or depth of the frustum ofcone
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|-
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|SPHERE
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|<math>4{\pi}r^2</math>
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|<math>4{\pi}r^2</math>
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|<math>\frac{4}{3}{\pi}r^3</math>
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|-
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|HEMISPHERE
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|<math>2{\pi}r^2</math>
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|<math>3{\pi}r^2</math>
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|<math>\frac{2}{3}{\pi}r^3</math>
 +
|-
 
|}
 
|}
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 +
[[Category:Mathematics]]

Latest revision as of 11:34, 4 November 2019

Algebraic Identities



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

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

Circle
Square

Where a is the side of a square

Rectangle

Where l & b are the length & breadth

Trapezium

Where a,b,c and d are the sides

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

Parallelogram

Where a & b are the sides of Parallelogram

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

Rhombus

Where a is the side of a rhombus

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

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

CUBOID
PRISM

1)EQUILATERAL TRIANGLE RIGHT PRISM

Where P=3a is the perimeter of base triangle

Where B= is the area of base

Where B=

2)SQUARE BASED RIGHT PRISM

Where P=4a is the perimeter of base square

Where B= is the area of base

Where B=

PYRAMID

1)EQUILATERAL TRIANGLE BASED RIGHT PYRAMID

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

Where B= is the area of base

Where B=

2)SQUARE BASED RIGHT PYRAMID

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

Where B= is the area of base

Where B=

CYLINDER

Where r is the radius of circular base

where "h" is the height of cylinder

CONE

Where l is the slant height

Where r is the radius of circular base

Where h is the height or depth of the cone

FRUSTUM OF CONE

Where l=

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

Where & are the radii of two bases

Where h is the height or depth of the frustum ofcone

SPHERE
HEMISPHERE