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.
In my opinion the the answer should be (A). I will attempt to give a detailed explanation below: Since it is a Hexagon, sum of internal angles is 720 using the formula: (n – 2) × 180, where 'n' is the number of sides of the polygon.
Therefore each internal angle is 120 degree. From this I say each triangle formed inside is an equilateral triangle. From (1), the area is 12 for each triangle. This is SUFFICIENT to conclude the hexagon having six triangles having an area of 12 each, has an area of 72.
When you solve any data sufficiency geometry question you should avoid graphics distorting your reasoning.
In this case the hexagon seems to be regular (all sides and angles are equal) and it affects the reasoning. Therefore you may conclude that all angles are equal (120⁰) but we have no facts that this conclusion can be based on.
The question statement gives us just the fact that we have a hexagon. It is just some arbitrary hexagon and can look in many different ways:
and many other different shapes. That gives us a clear idea why statement (1) is insufficient.
Statement (2) also doesn't imply that hexagon is regular (regular hexagon must have all equal sides AND angles). If we know that all sides are equal then hexagon can still have diverse shapes:
and many other variants.
So be careful with geometry graphics and always check if what you see is based on facts.
If all sides are equal, its a regular hexagon. An area of a regular hexagon can be considered 6 × area of the equilateral triangles. Thus using both the statements we could arrive at the solution . Hence option C is correct.
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