If the area of an equilateral …

{tex}Given ,\\ \\ Area \: \: of \: \: the \: \: equilateral \: \: \\ triangle \: \: is \: \: 36 \sqrt{3} \: cm {}^{2} \\ \\ To \: \: find \: \::- \: \:Height \: of \: \: the \\ equilateral \: \: triangle .\\ \\ \\ We \: \: know \: \: that ,\\ \\ Area \: of \: a \: equilateral \: \\ triangle \: \: = \frac{a {}^{2} }{4} \sqrt{3} \: \: \: \: ; where \: \: \: a \: \: \: \\ is \: \: the \: length \: of \: each \: side \: of \: the \\equlateral \: triangle.\\ \\ \\A.T.Q. \\ \\ \frac{a {}^{2} }{4} \sqrt{3} = 36 \sqrt{3} \\ \\ = > \frac{a {}^{2} }{4} = 36 \\ \\ = > a {}^{2} = 36 \times 4 \\ \\ = > a {}^{2} = (6) {}^{2} \times( 2) {}^{2} \\ \\ = > a = 6 \times 2 \\ \\ = > a = 12 \\ \\ \\ Length \: of \: each \: side \: of \: the \: \\ equilateral \: triangle \: is \: 12 \: cm{/tex}