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in Perimeter and Area of Plane Figures by (30.3k points)
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If the area of an equilateral triangle is 81√3 cm2 find its height.

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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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