Line 1: |
Line 1: |
| =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= |
Line 8: |
Line 24: |
| {|class="wikitable" | | {|class="wikitable" |
| |- | | |- |
− | |Shape | + | |Name |
| |Perimeter | | |Perimeter |
| |Area | | |Area |
Line 14: |
Line 30: |
| |Triangle | | |Triangle |
| |(a+b+c), where a, b, c are sides | | |(a+b+c), where a, b, c are sides |
− | |<math>\frac{1}{2}*b*h</math> | + | |<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*{\pi}*r</math> | + | |<math>2{\pi}r</math> |
− | |<math>{\pi}*r^2</math> | + | |<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 |
| |- | | |- |
− | |type square root
| |
− | |
| |
− | |<math>{\sqrt{25}}</math>
| |
| |} | | |} |
| | | |
− | ==LSA(CSA) TSA & VOLUME of solid Figures== | + | ==LSA(CSA) TSA & VOLUME of Solid Figures== |
| | | |
| {|class="wikitable" | | {|class="wikitable" |
Line 34: |
Line 75: |
| |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 |
Line 54: |
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 r_{1} & r_{2} are the radii of two bases(r_{1}>r_{2}) | + | 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> | | |<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 | | Where h is the height or depth of the frustum ofcone |
Line 68: |
Line 156: |
| |<math>\frac{2}{3}{\pi}r^3</math> | | |<math>\frac{2}{3}{\pi}r^3</math> |
| |- | | |- |
| + | |} |
| + | |
| + | [[Category:Mathematics]] |