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In the figure above, three segments are drawn to connect [#permalink]

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28 Jul 2009, 13:28

8

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A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

16% (02:09) correct
84% (00:46) wrong based on 140 sessions

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In the figure above, three segments are drawn to connect opposite vertices of a hexagon, forming six triangles. All three of these segments intersect at point A. What is the area of the hexagon?

1) One of the triangles has an area of 12. 2) All the sides of the hexagon are of equal length.

(E) Statement (1) is not sufficient because we do not know whether the hexagon is a regular hexagon (meaning that all 6 sides have the same length). We could only calculate the area if the hexagon could be divided into six congruent triangles.

Statement (2) is also insufficient because we are not given any numbers. So, it is impossible to calculate the area. Combined, the two statements are still insufficient. A hexagon could have six equal sides, yet not be a regular hexagon. Imagine pushing opposite sides of a regular hexagon closer to each other: the hexagon would flatten, while all the sides would remain the same length. One of the triangles within this flattened hexagon could have an area of 12, but not all of the triangles would have the same area. Therefore, we can't calculate the area, even by combining the statements, and the correct answer is choice (E).

Re: In the figure above, three segments are drawn to connect [#permalink]

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28 Jul 2009, 13:46

A

If the hexagon is a true hexagon and all sides equal, all angles equal, etc, then drawing three lines between the verticies should create 6 equal triangles, therefore, knowing the area of one, means we can determine the area of all 6 and thereby determine the area of the hexagon.

B is insufficient because even if the sides are equal, it's not new information. That's generally understood unless this is not a perfect hexagon where all sideas and angles are equal. If we cannot assume this is a pure hexagon, then neither is sufficient and they're not sufficient together, so the answer would be E. Otherwise, my answer is A.

coelholds wrote:

In the figure above, three segments are drawn to connect opposite vertices of a hexagon, forming six triangles. All three of these segments intersect at point A. What is the area of the hexagon?

1) One of the triangles has an area of 12. 2) All the sides of the hexagon are of equal length.

_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Re: In the figure above, three segments are drawn to connect [#permalink]

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28 Jul 2009, 15:04

IMO C,

Only the question stem will not suffice that it's a regular hexagon.

1) We dont know yet if its a regular hexagon yet. - NS 2) Says that it is a regular hexagon, but doesn't give us any other info. - NS 1+2) Regular hexagon with each triangle of area 12 . So Area = 12* 6 = 72 square units. Suff

Re: In the figure above, three segments are drawn to connect [#permalink]

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28 Jul 2009, 15:54

2

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As I said before, if we do not know that the sides are equal length AND the angles are all equal the answer should be E. Here is why:

We are still missing a piece of necessary information if we combine #1 and #2. I think we can all agree at this point that each independent statement is insufficient and the choices really come down to C or E.

If we want to use the information in #1 to multiply by 6 for the entire area of the hexagon, then we must be able to determine that all triangles created are equal, but in order to know that all triangles are equal, we must know that the sides of the hexagon are equal AND the angles are equal as well. Statement #2 only gives us the length of the sides as equal, and not the angles too. See the picture attached to my answer. The lines in the picture are all equal, but the triangles created in the interior are not equal, so by knowing the area of 1, we could not find the area of the others.

Answer E should be correct.

Attachment:

Hexagon.jpg [ 568.41 KiB | Viewed 4555 times ]

coelholds wrote:

In the figure above, three segments are drawn to connect opposite vertices of a hexagon, forming six triangles. All three of these segments intersect at point A. What is the area of the hexagon?

1) One of the triangles has an area of 12. 2) All the sides of the hexagon are of equal length.

Attachments

Hexagon.jpg [ 568.41 KiB | Viewed 4548 times ]

_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Re: In the figure above, three segments are drawn to connect [#permalink]

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28 Jul 2009, 18:58

Will go with E.. nothing is given about the 3 line segments intersecting each other.
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If you have made mistakes, there is always another chance for you. You may have a fresh start any moment you choose, for this thing we call "failure" is not the falling down, but the staying down.

Re: In the figure above, three segments are drawn to connect [#permalink]

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29 Jul 2009, 05:34

madeinafrica, no problem. You are just stuck in the same problem that I was.

Pay attention in what you wrote:

"The internal angles of a regular hexagon..." ops!!! Did the question say that it is a REGULAR hexagon?

No, and that is why we can not assume that it is. Even with a such beautiful and perfect image in the question. Remember, in DATA SUFFICIENCY questions, the image is not on scale.

So, what about an hexagon as jallenmorris has posted? Imagine the extremities even more close until forming almost a square. Calculate the area of the triangles, and you will see they are different. That is because it is not a REGULAR hexagon. So, you can have a hexagon with equal legs, but different angles. BUT, you can not have a hexagon with the equal angles and different legs!

It is clear now? If not, ask again, then I will try a more detail explanation....

PS.: If you liked the post, consider a kudo. I need just one more to access the GMATClub tests!!! Thank you

Re: In the figure above, three segments are drawn to connect [#permalink]

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15 Feb 2012, 04:52

Taking statement 2 into consideration,the hexagon is regular.If its regular with divided by 3 line segments intersecting with their ends separated equally will lead equal triangle areas.that way we can get 6*12 as the area.When have i gone wrong.Please help

Re: In the figure above, three segments are drawn to connect [#permalink]

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15 Feb 2012, 07:08

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gmatnerd wrote:

Taking statement 2 into consideration,the hexagon is regular.If its regular with divided by 3 line segments intersecting with their ends separated equally will lead equal triangle areas.that way we can get 6*12 as the area.When have i gone wrong.Please help

What if I squeeze some air out of the hexagon, it still has equal sides but the inside diagonals will differ, and nowhere does the question say that the segments are equal. Think, Think ! Its a nice question. Even I was a bit apprehensive about it, but I guess the diagram is misleading, it makes you think that the segments are equal in length. If you still don't get it, look at the digram below.

Re: In the figure above, three segments are drawn to connect [#permalink]

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15 Feb 2012, 18:13

Thanks a lot for the eplination.I was still not convinced(may be because i dont have the math to prove either way) so went and checked in some math forum.2 hexagons are congruent IFF both sides and all internal angles are equal (which means its possible to construct more than one hexagon with equal sides).This means that the area cannot be estimated from just knowing the side length and all of them are equal

Re: In the figure above, three segments are drawn to connect [#permalink]

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04 Apr 2015, 23:27

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Re: In the figure above, three segments are drawn to connect [#permalink]

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26 Aug 2016, 19:24

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