# List of formulae

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# Algebraic Identities

• ${\displaystyle (a+b)(a-b)=a^{2}-b^{2}}$
• ${\displaystyle (a+b)^{2}=a^{2}+2ab+b^{2}}$
• ${\displaystyle (a-b)^{2}=a^{2}-2ab+b^{2}}$
• ${\displaystyle (x+a)(x+b)=x^{2}+x(a+b)+ab}$
• ${\displaystyle (x+a)(x+b)(x+c)=x^{3}+x^{2}(a+b+c)+x(ab+bc+ca)+abc}$
• ${\displaystyle (a+b)^{3}=a^{3}+3ab(a+b)+b^{3}}$
• ${\displaystyle (a-b)^{3}=a^{3}-3ab(a-b)-b^{3}}$
• ${\displaystyle a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})}$
• ${\displaystyle a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})}$
• ${\displaystyle (a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2ab+2bc+2ca}$
• ${\displaystyle a^{4}+a^{2}b^{2}+b^{4}=(a^{2}+b^{2}+ab)(a^{2}+b^{2}-ab)}$
• ${\displaystyle (a+b+c)^{3}-a^{3}-b^{3}-c^{3}=3(a+b)(b+c)(c+a)}$
• ${\displaystyle (a+b)(b+c)(c+a)=(a+b+c)(ab+bc+ca)-abc}$

# Mensuration

## Area and Perimeter of Plane Figures

 Name Perimeter Area Triangle (a+b+c), where a, b, c are sides ${\displaystyle {\frac {1}{2}}bh}$ where "h" is the height from any vertex to the opposite side "b" Circle ${\displaystyle 2{\pi }r}$ ${\displaystyle {\pi }r^{2}}$ Square ${\displaystyle 4a}$ Where a is the side of a square ${\displaystyle a^{2}}$ Rectangle ${\displaystyle 2(l+b)}$ Where l & b are the length & breadth ${\displaystyle lb}$ Trapezium ${\displaystyle (a+b+c+d)}$ Where a,b,c and d are the sides ${\displaystyle {\frac {1}{2}}h(a+b)}$ Where a and b are parallel sides of trapezium. And h is the perpendicular distance between two parallel sides. Parallelogram ${\displaystyle 2(a+b)}$ Where a & b are the sides of Parallelogram ${\displaystyle bh}$ Where b is base and h is the perpendicular distance between base b and its parallel side. Rhombus ${\displaystyle 4a}$ Where a is the side of a rhombus ${\displaystyle {\frac {1}{2}}(d_{1}d_{2})}$ 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 ${\displaystyle 4l^{2}}$ Where lenght(l)=breadth(b)=height(h) ${\displaystyle 6l^{2}}$ ${\displaystyle l^{3}}$ CUBOID ${\displaystyle 2h(l+b)}$ ${\displaystyle 2(lb+bh+lh)}$ ${\displaystyle lbh}$ PRISM 1)EQUILATERAL TRIANGLE RIGHT PRISM ${\displaystyle Ph}$ Where P=3a is the perimeter of base triangle ${\displaystyle 2B+Ph}$ Where B=${\displaystyle {\frac {{\sqrt {3}}a^{2}}{4}}}$ is the area of base ${\displaystyle Bh}$ Where B=${\displaystyle {\frac {{\sqrt {3}}a^{2}}{4}}}$ 2)SQUARE BASED RIGHT PRISM ${\displaystyle Ph}$ Where P=4a is the perimeter of base square ${\displaystyle 2B+Ph}$ Where B=${\displaystyle a^{2}}$ is the area of base ${\displaystyle Bh}$ Where B=${\displaystyle a^{2}}$ PYRAMID 1)EQUILATERAL TRIANGLE BASED RIGHT PYRAMID ${\displaystyle {\frac {1}{2}}Pl}$ Where P=3a is the perimeter of base triangle l is the slant height ${\displaystyle B+{\frac {1}{2}}Pl}$ Where B=${\displaystyle {\frac {{\sqrt {3}}a^{2}}{4}}}$ is the area of base ${\displaystyle {\frac {1}{3}}Bh}$ Where B=${\displaystyle {\frac {{\sqrt {3}}a^{2}}{4}}}$ 2)SQUARE BASED RIGHT PYRAMID ${\displaystyle {\frac {1}{2}}Pl}$ Where P=4a is the perimeter of base square l is the slant height ${\displaystyle B+{\frac {1}{2}}Pl}$ Where B=${\displaystyle a^{2}}$ is the area of base ${\displaystyle {\frac {1}{3}}Bh}$ Where B=${\displaystyle a^{2}}$ CYLINDER ${\displaystyle 2{\pi }rh}$ Where r is the radius of circular base ${\displaystyle 2{\pi }r(r+h)}$ where "h" is the height of cylinder ${\displaystyle {\pi }r^{2}h}$ CONE ${\displaystyle {\pi }rl}$ Where l is the slant height ${\displaystyle {\pi }r(l+r)}$ Where r is the radius of circular base ${\displaystyle {\frac {1}{3}}{\pi }r^{2}h}$ Where h is the height or depth of the cone FRUSTUM OF CONE ${\displaystyle {\pi }(r_{1}+r_{2})l}$ Where l=${\displaystyle {\sqrt {h^{2}+(r_{1}-r_{2})^{2}}}}$ $\displaystyle π{{(r_{1}+r_{2})l+r_{1}^2+r_{2}^2}}$ Where ${\displaystyle r_{1}}$ & ${\displaystyle r_{2}}$ are the radii of two bases${\displaystyle (r_{1}>r_{2})}$ ${\displaystyle {\frac {1}{3}}{\pi }h(r_{1}^{2}+r_{2}^{2}+r_{1}r_{2})}$ Where h is the height or depth of the frustum ofcone SPHERE ${\displaystyle 4{\pi }r^{2}}$ ${\displaystyle 4{\pi }r^{2}}$ ${\displaystyle {\frac {4}{3}}{\pi }r^{3}}$ HEMISPHERE ${\displaystyle 2{\pi }r^{2}}$ ${\displaystyle 3{\pi }r^{2}}$ ${\displaystyle {\frac {2}{3}}{\pi }r^{3}}$