Area of equilateral triangle = \(81\sqrt{3}\) cm2
Area of equilateral triangle = \((\frac{\sqrt{3}}{4}\times a^2)\), where a is the length of the side
\(\Rightarrow 81\sqrt{3}=\frac{\sqrt{3}}{4}\times a^2\)
\(\Rightarrow\) 324 = a2
\(\Rightarrow\) a = 18 cm
Height of triangle = \(\frac{\sqrt{3}}{2}\times a^2\)
= \(\frac{\sqrt{3}}2{}\times18\)
= \(9\sqrt{3}\) cm