I think the answer is D.
Statement I
All the six sides of the hexagon are equal. Therefore the angle formed by the vertice at center will be 60, therefore all the alngles will be equal. Hence Sufficient.
Statement II
The each side is equal. Hence Sufficient.
Answer D.
Whats the OA?
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Hexagon Geometry
Source: Beat The GMAT — Data Sufficiency |
1) All sides of the hexagon have the same length.
The sides can have the same length but the three segments may be really different. Imagine the horizontal one is larger, the hexagon will be flat and some of the triangles are not equilateral. The problem is we do not know what can look like the angles of the hexagon.
2) The three segments drawn between the opposite vertices are the same length.
In this case, you could have really different one side lengths. the angles of the vertices on A may have different angles.
1)and2)
With 1) you know that the angles on A are the same to get same length of sides.
With 2) you are sure that the triangles are isoceles .
So with 1) and 2) triangles are equilaterals.
I join counter-examples, I will personnally use graphs next time I think it can be efficient coz I chose D.
Thanks for your answer, hope this explanation is clear.
The sides can have the same length but the three segments may be really different. Imagine the horizontal one is larger, the hexagon will be flat and some of the triangles are not equilateral. The problem is we do not know what can look like the angles of the hexagon.
2) The three segments drawn between the opposite vertices are the same length.
In this case, you could have really different one side lengths. the angles of the vertices on A may have different angles.
1)and2)
With 1) you know that the angles on A are the same to get same length of sides.
With 2) you are sure that the triangles are isoceles .
So with 1) and 2) triangles are equilaterals.
I join counter-examples, I will personnally use graphs next time I think it can be efficient coz I chose D.
Thanks for your answer, hope this explanation is clear.
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I have a DS question on similar lines:pepeprepa wrote:DS with an hexagon
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 a point A. What is the area of the hexagon?
(1) One of the triangles has an area of 12
(2) All sides of the hexagon are of equal length
OA is E.............can any one please explain??
