Question:
Find the area of an equilateral triangle of side 6 cm.
Solution:
Area of an equilateral traingle $=\left(\frac{\sqrt{3}}{4} \times(\text { side })^{2}\right)$ square units
$=\left(\frac{\sqrt{3}}{4} \times 6 \times 6\right) \mathrm{cm}^{2}$
$=\left(\frac{\sqrt{3}}{4} \times 36\right) \mathrm{cm}^{2}$
$=9 \sqrt{3} \mathrm{~cm}^{2}$
Hence, the area of an equilateral triangle is $9 \sqrt{3} \mathrm{~cm}^{2}$.
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