140 views

1 vote

Let the side of hexagon be $x \; \text{cm}.$

The area of regular hexagon $ = 6 \times \frac{\sqrt{3}}{4} x^{2}$

Now, $6 \times \frac{\sqrt{3}}{4} x^{2} = \frac{\sqrt{3}}{4} (12)^{2}$

$ \Rightarrow 6x^{2} = 12 \times 12 $

$\Rightarrow x^{2} = 24 $

$ \Rightarrow x = \sqrt{24}$

$ \Rightarrow \boxed{ x = 2 \sqrt{6} \; \text{cm}}$

Correct Answer $: \text{B}$

$\textbf{PS:}$ The regular hexagon

The $\triangle \text{ABC}$ are equilateral triangle.

- The area of an equilateral triangle $ = \frac{\sqrt{3}}{4} \times \text{(Side)}^{2}$
- The area of regular hexagon $ = 6 \times \frac{\sqrt{3}}{4} \times \text{(Side)}^{2}$