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 sides of the hexagon are of equal length.

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

D. Either statement BY ITSELF is sufficient to answer the question.

E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(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).

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**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.

Please confirm.