CAT 2021 Slot 1 QA Question & Solution

GeometryEasy

Question

If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is

Options

$4\sqrt{6}$

$6\sqrt{6}$

$\sqrt{6}$

$2\sqrt{6}$

Solution

Area of a regular hexagon = $\frac{3\sqrt{3}}{2}x^2$

Area of an equilateral triangle = $\frac{\sqrt{3}}{4}\left(a\right)^2$ ; where a = side of the triangle

Since the area of the two figures are equal, we can equate them as folllows: $\frac{3\sqrt{3}}{2}x^2=\frac{\sqrt{3}}{4}\left(12\right)^2$

On simplifying: $x^2=24$

$\therefore\ x=2\sqrt{6}$