Difference between revisions of "List of formulae"
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=Algebraic Identities= | =Algebraic Identities= | ||
+ | *<math>(a+b)(a-b)=a^2-b^2</math> | ||
+ | *<math>(a+b)^2=a^2+2ab+b^2</math> | ||
+ | *<math>(a-b)^2=a^2-2ab+b^2</math> | ||
+ | *<math>(x+a)(x+b)=x^2+x(a+b)+ab</math> | ||
+ | *<math>(x+a)(x+b)(x+c)=x^3+x^2(a+b+c)+x(ab+bc+ca)+abc</math> | ||
+ | *<math>(a+b)^3=a^3+3ab(a+b)+b^3</math> | ||
+ | *<math>(a-b)^3=a^3-3ab(a-b)-b^3</math> | ||
+ | *<math>a^3+b^3=(a+b)(a^2-ab+b^2)</math> | ||
+ | *<math>a^3-b^3=(a-b)(a^2+ab+b^2)</math> | ||
+ | *<math>(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca</math> | ||
+ | *<math>a^4+a^2b^2+b^4=(a^2+b^2+ab)(a^2+b^2-ab)</math> | ||
+ | *<math>(a+b+c)^3-a^3-b^3-c^3=3(a+b)(b+c)(c+a)</math> | ||
+ | *<math>(a+b)(b+c)(c+a)=(a+b+c)(ab+bc+ca)-abc</math><br> | ||
+ | |||
+ | |||
=Geometric Results= | =Geometric Results= | ||
+ | |||
=Formulae for commercial arithmetic= | =Formulae for commercial arithmetic= | ||
=Statistical Formulae= | =Statistical Formulae= | ||
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{|class="wikitable" | {|class="wikitable" | ||
|- | |- | ||
− | | | + | |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 | ||
− | |<math>\frac{1}{2} | + | |<math>\frac{1}{2}bh</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" | ||
|- | |- | ||
|Circle | |Circle | ||
− | |<math>2 | + | |<math>2{\pi}r</math> |
− | |<math>{\pi} | + | |<math>{\pi}r^2</math> |
+ | |- | ||
+ | |Square | ||
+ | |<math>4a</math> | ||
+ | Where a is the side of a square | ||
+ | |<math>a^2</math> | ||
+ | |- | ||
+ | |Rectangle | ||
+ | |<math>2(l+b)</math> | ||
+ | Where l & b are the length & breadth | ||
+ | |<math>lb</math> | ||
+ | |- | ||
+ | |Trapezium | ||
+ | |<math>(a+b+c+d)</math> | ||
+ | Where a,b,c and d are the sides | ||
+ | |<math>\frac{1}{2}h(a+b)</math> | ||
+ | Where a and b are parallel sides of trapezium. And h is the perpendicular distance between two parallel sides. | ||
+ | |- | ||
+ | |Parallelogram | ||
+ | |<math>2(a+b)</math> | ||
+ | Where a & b are the sides of Parallelogram | ||
+ | |<math>bh</math> | ||
+ | Where b is base and h is the perpendicular distance between base b and its parallel side. | ||
+ | |- | ||
+ | |Rhombus | ||
+ | |<math>4a</math> | ||
+ | Where a is the side of a rhombus | ||
+ | |<math>\frac{1}{2}(d_{1}d_{2})</math> | ||
+ | Where d1 and d2 are diagonals of rhombus | ||
|- | |- | ||
− | |||
− | |||
− | |||
|} | |} | ||
− | ==LSA(CSA) TSA & VOLUME of | + | ==LSA(CSA) TSA & VOLUME of Solid Figures== |
{|class="wikitable" | {|class="wikitable" | ||
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|TSA in sq.units | |TSA in sq.units | ||
|VOLUME in cubic units | |VOLUME in cubic units | ||
+ | |- | ||
+ | |CUBE | ||
+ | |<math>4l^2</math> | ||
+ | Where lenght(l)=breadth(b)=height(h) | ||
+ | |<math>6l^2</math> | ||
+ | |<math>l^3</math> | ||
+ | |- | ||
+ | |CUBOID | ||
+ | |<math>2h(l+b)</math> | ||
+ | |<math>2(lb+bh+lh)</math> | ||
+ | |<math>lbh</math> | ||
+ | |- | ||
+ | |PRISM | ||
+ | 1)EQUILATERAL TRIANGLE RIGHT PRISM | ||
+ | |<math>Ph</math> | ||
+ | Where P=3a is the perimeter of base triangle | ||
+ | |<math>2B+Ph</math> | ||
+ | Where B=<math>\frac{\sqrt{3}a^2}{4}</math> is the area of base | ||
+ | |<math>Bh</math> | ||
+ | Where B=<math>\frac{\sqrt{3}a^2}{4}</math> | ||
+ | |- | ||
+ | |2)SQUARE BASED RIGHT PRISM | ||
+ | |<math>Ph</math> | ||
+ | Where P=4a is the perimeter of base square | ||
+ | |<math>2B+Ph</math> | ||
+ | Where B=<math>a^2</math> is the area of base | ||
+ | |<math>Bh</math> | ||
+ | Where B=<math>a^2</math> | ||
+ | |- | ||
+ | |PYRAMID | ||
+ | 1)EQUILATERAL TRIANGLE BASED RIGHT PYRAMID | ||
+ | |<math>\frac{1}{2}Pl</math> | ||
+ | Where P=3a is the perimeter of base triangle<br> | ||
+ | l is the slant height | ||
+ | |<math>B+\frac{1}{2}Pl</math> | ||
+ | Where B=<math>\frac{\sqrt{3}a^2}{4}</math> is the area of base | ||
+ | |<math>\frac{1}{3}Bh</math> | ||
+ | Where B=<math>\frac{\sqrt{3}a^2}{4}</math> | ||
+ | |- | ||
+ | |2)SQUARE BASED RIGHT PYRAMID | ||
+ | |<math>\frac{1}{2}Pl</math> | ||
+ | Where P=4a is the perimeter of base square<br> | ||
+ | l is the slant height | ||
+ | |<math>B+\frac{1}{2}Pl</math> | ||
+ | Where B=<math>a^2</math> is the area of base | ||
+ | |<math>\frac{1}{3}Bh</math> | ||
+ | Where B=<math>a^2</math> | ||
|- | |- | ||
|CYLINDER | |CYLINDER | ||
|<math>2{\pi}rh</math> | |<math>2{\pi}rh</math> | ||
+ | Where r is the radius of circular base | ||
|<math>2{\pi}r(r+h)</math> | |<math>2{\pi}r(r+h)</math> | ||
where "h" is the height of cylinder | where "h" is the height of cylinder | ||
Line 45: | Line 134: | ||
Where l is the slant height | Where l is the slant height | ||
|<math>{\pi}r(l+r)</math> | |<math>{\pi}r(l+r)</math> | ||
+ | Where r is the radius of circular base | ||
|<math>\frac{1}{3}{\pi}r^2h</math> | |<math>\frac{1}{3}{\pi}r^2h</math> | ||
+ | Where h is the height or depth of the cone | ||
|- | |- | ||
|FRUSTUM OF CONE | |FRUSTUM OF CONE | ||
Line 51: | Line 142: | ||
Where l=<math>\sqrt{h^2+(r_{1}-r_{2})^2}</math> | Where l=<math>\sqrt{h^2+(r_{1}-r_{2})^2}</math> | ||
|<math>π{{(r_{1}+r_{2})l+r_{1}^2+r_{2}^2}}</math> | |<math>π{{(r_{1}+r_{2})l+r_{1}^2+r_{2}^2}}</math> | ||
− | Where | + | Where <math>r_{1}</math> & <math>r_{2}</math> are the radii of two bases<math>(r_{1}>r_{2})</math> |
− | |<math>\frac{1}{3}{\pi}h(r_{1}^2+r_{2}^2+r_{1}r_{2}) | + | |<math>\frac{1}{3}{\pi}h(r_{1}^2+r_{2}^2+r_{1}r_{2})</math> |
+ | Where h is the height or depth of the frustum ofcone | ||
+ | |- | ||
+ | |SPHERE | ||
+ | |<math>4{\pi}r^2</math> | ||
+ | |<math>4{\pi}r^2</math> | ||
+ | |<math>\frac{4}{3}{\pi}r^3</math> | ||
+ | |- | ||
+ | |HEMISPHERE | ||
+ | |<math>2{\pi}r^2</math> | ||
+ | |<math>3{\pi}r^2</math> | ||
+ | |<math>\frac{2}{3}{\pi}r^3</math> | ||
+ | |- | ||
|} | |} | ||
+ | |||
+ | [[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 |
Where B= is the area of base |
Where B= |
2)SQUARE BASED RIGHT PYRAMID |
Where P=4a is the perimeter of base square |
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 (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\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 |