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# Which of the following could be the area of a regular hexagon in which

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6815
GMAT 1: 760 Q51 V42
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Which of the following could be the area of a regular hexagon in which  [#permalink]

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02 Jan 2019, 00:47
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35% (medium)

Question Stats:

65% (01:04) correct 35% (01:36) wrong based on 34 sessions

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[Math Revolution GMAT math practice question]

Which of the following could be the area of a regular hexagon in which the length of the equal sides is an integer?

$$A. \frac{√3}{6}$$
$$B. \frac{√3}{5}$$
$$C. \frac{√3}{4}$$
$$D. 6√3$$
$$E. \frac{3√3}{4}$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 15 Jan 2018 Posts: 101 Location: India Concentration: General Management, Finance GMAT 1: 720 Q50 V37 WE: Information Technology (Computer Software) Re: Which of the following could be the area of a regular hexagon in which [#permalink] ### Show Tags 02 Jan 2019, 00:59 1 Important Note: A regular hexagon has 6 equal equilateral triangles. We know the area of an equilateral triangles (√3/4)xa^2, where a is the length of the side Hence, Area of regular hexagon = 6x (√3/4)xa^2 = (3√3)/2 a^2 For a = 2, the above equation becomes 6√3. Hence, the Correct Answer is Option D.6√3 _________________ In order to reach the next tier, I need kudos. Please provide me with kudos in case you like my post. Thank you VP Joined: 18 Aug 2017 Posts: 1229 Location: India Concentration: Sustainability, Marketing WE: Marketing (Energy and Utilities) Re: Which of the following could be the area of a regular hexagon in which [#permalink] ### Show Tags 02 Jan 2019, 16:18 MathRevolution wrote: [Math Revolution GMAT math practice question] Which of the following could be the area of a regular hexagon in which the length of the equal sides is an integer? $$A. \frac{√3}{6}$$ $$B. \frac{√3}{5}$$ $$C. \frac{√3}{4}$$ $$D. 6√3$$ $$E. \frac{3√3}{4}$$ for a hexagon of equal sides the area can be calculated using formula sqrt3 * x^2/2 this has ben derieved from equilateral triangle formula (sqrt3*x^2/4) * 6 since given that x is an integer so only at x=2 we get option D 6 sqrt3 IMOD _________________ If you liked my solution then please give Kudos. Kudos encourage active discussions. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6815 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following could be the area of a regular hexagon in which [#permalink] ### Show Tags 04 Jan 2019, 00:18 Attachment: 1.4.png [ 11.63 KiB | Viewed 154 times ] => Let $$n$$ be the side-length of a regular hexagon. Then the area of the shaded equilateral triangle is $$(\frac{√3}{4})n^2$$ and the area of the regular hexagon is $$(\frac{6√3}{4})n^2 = (\frac{3√3}{2})n^2$$ . If $$n = 2$$, then $$(\frac{3√3}{2})n^2 = (\frac{3√3}{2})2^2 =6√3$$. None of the other values are possible for integer values of $$n$$. Therefore, the answer is D. Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: Which of the following could be the area of a regular hexagon in which &nbs [#permalink] 04 Jan 2019, 00:18
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