In the figure above, three segments are drawn to connect

yes but they did not said that it was a "true one, with all side equal"

Answer should be C.
we can only solve the pb if we know that it is a regular hexagone. exemple of an hexagone that is not regular...

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

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.

You certainly do have a point there.

What is the OA and explaination?

Will go with E.. nothing is given about the 3 line segments intersecting each other.

I would go with E too. What is the OA?

What I wanted to point out is that If all side of an hexagone are equal, then all angle are also equal.
hence we can solve this question.

Like a triangle, If a triangle has all sides equals, then the angles are equals too.

am I wrong? if this assumption is wrong therefore answer is E

what is OA?

Yes guys OA is E

That is why I have posted this question here.

This took me a while to believe.

The fact is that you need to visualize that figure that jallenmorris have attached.

Congrats!!!!

Thanks guy

Could some one telle me where i'm wrong?
on wiki i can find this:

"The internal angles of a regular hexagon (where all of the sides are the same) are all 120° and the hexagon has 720 degrees T."

So I still think that if all side of an hexagon are the same, then all angles are equal.
hence I do not understant why answer is not C.

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

Here is another example of a hexagon with equal sides but unequal angles.

Only with regard to a triangle can we assume equal angles with equal sides. No other polygon fits into this situation.

Thanks. Kudos to you.

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

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

TAKEAWAY

Only triangle is the polygon where equal sides proves regular polygon.
"If all sides of a triangle are equal, triangle is equilateral with all angles equal. It is a regular polygon."

"For polygons (other than triangle), equality of sides doesn't make it a regular polygon."
For example in quadrilateral, all sides equal proves Quadrilateral to be rhombus, not square.
we need additional information to prove the same.

Statement 1) obviously not sufficient. We have no indication that all triangles are same i.e. no indication that it is a regular hexagon
Statement 2) All sides maybe equal, but this is not enough to constrain the hexagon to be a regular hexagon! The angles could still be different.
Combining neither gives any indication that all triangles have same area (12) nor any indication that all angles are same. So not sufficient.
Ans E