CAT Exam 2021 Slot 1 Solved Paper

Area of regular hexagon $=\frac{3\sqrt{3}}{2}\times {\mathrm{x}}^2$
Area of an equilateral triangle = $\frac{\sqrt{3}}{4}{\left(\mathrm{a}\right)}^2$ ; where a= side of triangle
since the area of the two figures are equal, we can equate them as following :
$\frac{3\sqrt{3}}{2}\times {\mathrm{x}}^2=\frac{\sqrt{3}}{4}{\left(12\right)}^2$
On simplifying: ${\mathrm{x}}^2+24$
$\therefore \mathrm{x}=2\sqrt{6}$