CAT 2021 Slot 1 · Quant · Question 1
CAT 2021 Slot 1 previous year question on Mensuration 2D, with the answer and a step-by-step solution.
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
- A
4\sqrt{6}
- B
2\sqrt{6}
- C
6\sqrt{6}
- D
\sqrt{6}
Pick an option, then check.
Answer & solution
Answer: Option B
Area of the equilateral triangle =\frac{\sqrt{3}}{4}\times{12}^{2}=36\sqrt{3}.
The area of a regular hexagon of side a is \frac{3\sqrt{3}}{2}{a}^{2}.
Equating the two, \frac{3\sqrt{3}}{2}{a}^{2}=36\sqrt{3}, so {a}^{2}=24 and a=2\sqrt{6} cm.
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