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Q.
The height of an equilateral triangle is $9 \mathrm{~cm}$. Find its area (in $\mathrm{cm}^2$ ).
Mensuration
Solution:
Let the side of the equilateral triangle be $a \mathrm{~cm}$.
$ \text { Given: } \frac{\sqrt{3}}{2} a=9 \Rightarrow a=\frac{18}{\sqrt{3}} \Rightarrow a=6 \sqrt{3} $
$\therefore \text { Area }=\frac{\sqrt{3}}{4} a^2=\frac{\sqrt{3}}{4}(6 \sqrt{3})^2=27 \sqrt{3} \mathrm{~cm}^2$