CAT 2021 Slot 1 QA Question 7: 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

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

Accepted Answer

Let the side of the regular hexagon be $s$.
Area of a regular hexagon of side $s$ is six times the area of an equilateral triangle of side $s$.
$6 	imes \dfrac{\sqrt{3}}{4}s^2 = \dfrac{3\sqrt{3}}{2}s^2$
Area of the equilateral triangle of side 12 cm is
$\dfrac{\sqrt{3}}{4} 	imes 12^2 = 36\sqrt{3}$