The height of an equilateral triangle measures 9 cm. Find its area, correct to 2 places of decimal. $(T a k e \sqrt{3} = 1.732.)$

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Solution

The height of the equilateral triangle = 9 cm
Thus, we have:
Height = $\frac{\sqrt{3}}{2} \times S i d e$
⇒9 = $\frac{\sqrt{3}}{2} \times S i d e$
⇒Side = $\frac{18}{\sqrt{3}}$
Also,
Area of equilateral triangle = $\frac{\sqrt{3}}{4} \times (S i d e^{2})$ = $\frac{\sqrt{3}}{4} \times (\frac{18}{\sqrt{3}})^{2}$ = 46.76 $c m^{2}$

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