# Choose the correct answer of the following question:

Question:

Choose the correct answer of the following question:

The height of an equilateral triangle is $3 \sqrt{3} \mathrm{~cm}$. Its area is

(a) $6 \sqrt{3} \mathrm{~cm}^{2}$

(b) $27 \mathrm{~cm}^{2}$

(c) $9 \sqrt{3} \mathrm{~cm}^{2}$

(d) $27 \sqrt{3} \mathrm{~cm}^{2}$

Solution:

Let the side of the equilateral triangle be $x$.

As, area of the equilateral triangle $=\frac{\sqrt{3}}{4} \times(\text { side })^{2}$

$\Rightarrow \frac{1}{2} \times$ Base $\times$ Height $=\frac{\sqrt{3}}{4} \times x^{2}$

$\Rightarrow \frac{1}{2} \times x \times 3 \sqrt{3}=\frac{x^{2} \sqrt{3}}{4}$

$\Rightarrow \frac{3 x \sqrt{3}}{2}=\frac{x^{2} \sqrt{3}}{4}$

$\Rightarrow \frac{3 \sqrt{3}}{2}=\frac{x \sqrt{3}}{4}$

$\Rightarrow x=\frac{3 \sqrt{3} \times 4}{2 \sqrt{3}}$

$\Rightarrow x=6 \mathrm{~cm}$

Now, the area of the triangle $=\frac{\sqrt{3}}{4} \times 6^{2}$

$=\frac{\sqrt{3}}{4} \times 36$

$=9 \sqrt{3} \mathrm{~cm}^{2}$

Hence, the correct answer is option (c).