Proof of area of an equilateral triangle whose side is a.

1.	Proof of area of an equilateral triangle whose side is a.
Answer» \'a\' = a, \'b\' = a, \'c\' = a{tex}\\therefore{/tex}{tex}s=\\frac{^{\\prime} a^{\\prime}+b^{\\prime}+^{\\prime} c^{\\prime}}{2}{/tex}s =\xa0{tex}\\frac{a+a+a}{2}{/tex}\xa0=\xa0{tex}\\frac{3a}{2}{/tex}\xa0{tex}\\therefore{/tex}\xa0Area of the equilateral triangle=\xa0{tex}\\sqrt{s\\left(s-\' a^{\\prime}\\right)\\left(s-^{\\prime} b^{\\prime}\\right)\\left(s-^{\\prime} c^{\\prime}\\right)}{/tex}=\xa0{tex}\\sqrt{\\frac{3 a}{2}\\left(\\frac{3 a}{2}-a\\right)\\left(\\frac{3 a}{2}-a\\right)\\left(\\frac{3 a}{2}-a\\right)}{/tex}=\xa0{tex}\\sqrt{\\frac{3 a}{2}\\left(\\frac{a}{2}\\right)\\left(\\frac{a}{2}\\right)\\left(\\frac{a}{2}\\right)}{/tex}=\xa0{tex}\\frac{\\sqrt{3} a^{2}}{4}{/tex}\xa0square units.

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