The height of an equilateral triangle is 6 cm. Find its area.
Question:

The height of an equilateral triangle is 6 cm. Find its area.  $[$ Take $\sqrt{3}=1.73]$

Solution:

Let the side of the equilateral triangle be x cm.

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

Also, the area of the triangle $=\frac{1}{2} \times$ Base $\times$ Height $=\frac{1}{2} \times x \times 6=3 x$

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

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

$\Rightarrow x=\frac{12}{\sqrt{3}}$

$\Rightarrow x=\frac{12}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$

$\Rightarrow x=\frac{12 \sqrt{3}}{3}$

$\Rightarrow x=4 \sqrt{3} \mathrm{~cm}$

Now, area of the equilateral triangle $=3 x$

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

$=12 \sqrt{3}$

$=12 \times 1.73$

$=20.76 \mathrm{~cm}^{2}$