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# CAT 2021 Quant Question [Slot 1] with Solution 02

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
1. $4\sqrt 6$
2. $6\sqrt 6$
3. $\sqrt 6$
4. $2\sqrt 6$
Option: 4
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: ${x^2} = 24\;$ $\therefore \;x = 2\sqrt 6$
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## CAT 2021 Quant questions with Solutions

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