If the area of an equilateral triangle is 81√3 cm2 find its height.

1.	If the area of an equilateral triangle is 81√3 cm2 find its height.
Answer» 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

Answer»

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

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