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

My question: On the gmat, will it specifically state whether the hexagon is a regular hexagon or not? I assumed that when you mentioned hexagon it was a regular hexagon.

With the problem at hand, AEK, you don't need to know if the hexagon is regular or not. All of the necessary information is provided. However, on the GMAT when you actually encounter a problem that involves a geometric figure that is regular, and, it is required that you know the latter in order to solve the problem, then yes, the GMAT question will provide you with that information.

A regular hexagon has all its sides equal to each other. The one shown in your example does not have all its sides equal and hence doesnot justify your explanation.

I understand the question, but I think "three segments connecting opposite vertices of a hexagon intersect at a point" means that the hexagon is a regular hexagon!

I understand the question, but I think "three segments connecting opposite vertices of a hexagon intersect at a point" means that the hexagon is a regular hexagon!

No. You can see that if you draw various cases of 3 arbitrary segments that intersect in one point, then you just need to connect the ends of the segments to create various hexagons.

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