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If the length of one side of a regular hexagon (all

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Carcass
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If the length of one side of a regular hexagon (all [#permalink] New post   06 Aug 2017, 11:01
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If the length of one side of a regular hexagon (all sides and angles equal) is 8, what is the area of the hexagon ?

A. 48

B. \(36 \sqrt{3}\)

C. \(48 \sqrt{2}\)

D.\(96 \sqrt{3}\)

E. \(128 \sqrt{2}\)
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IlCreatore
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Re: If the length of one side of a regular hexagon (all [#permalink] New post   19 Sep 2017, 06:31
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Is it right to see the hexagon as made of six equilateral triangles each of area \(\frac{8*4sqrt(3)}{2} = 16sqrt(3)\) so that the area of the hexagon is six times the area of a triangle, i.e. \(6*16sqrt(3)=96sqrt(3)\)?
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Re: If the length of one side of a regular hexagon (all [#permalink] New post   17 Jul 2018, 13:23
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IlCreatore wrote:
Is it right to see the hexagon as made of six equilateral triangles each of area \(\frac{8*4sqrt(3)}{2} = 16sqrt(3)\) so that the area of the hexagon is six times the area of a triangle, i.e. \(6*16sqrt(3)=96sqrt(3)\)?



Could you please explain why you assumed that fact about hexagon while it's not given?
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Re: If the length of one side of a regular hexagon (all [#permalink] New post   17 Jul 2018, 13:34
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The fact that is not mentioned in the stem or elsewhere, then nothing avoid you to make this assumption about the hexagon and triangles.

It is just another way to solve the problem. The lesson you might learn from this is that flexibility in quant solving problem is king.

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Re: If the length of one side of a regular hexagon (all [#permalink] New post   17 Jul 2018, 22:31
Carcass wrote:
The fact that is not mentioned in the stem or elsewhere, then nothing avoid you to make this assumption about the hexagon and triangles.

It is just another way to solve the problem. The lesson you might learn from this is that flexibility in quant solving problem is king.

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Thanks Carcass. So can we make the same assumption a bout all regular polygons n (number of sides)>3?
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Re: If the length of one side of a regular hexagon (all [#permalink] New post   18 Jul 2018, 01:21
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yes. octagon and so on.......
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Re: If the length of one side of a regular hexagon (all [#permalink] New post   09 May 2020, 09:49
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Learn this formula:

Area of regular hexagon = \(s^2*\)\(\frac{3\sqrt{3}}{2}\), where s is one side.

Apply and answer D
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Re: If the length of one side of a regular hexagon (all [#permalink] New post   15 Aug 2021, 13:05
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