Hello!

I completely agree with x2suresh; I think his answer is correct, that the area is \(16sqrt3+24\). What I've done here is a series of illustrations that go along with his explanation.

The original:

The diagram seems to imply the necessary symmetry to get that it's equilateral.

Bisecting angle BCA. By extending the line, I convinced myself that we truly were bisecting it.

Thus, angle DCR must be 30 degrees, which leaves angle CRD to be 60 degrees. Recall that the short side, that opposite the 30, was of length 2.

Here's a handy reminder of the 30-60-90 triangle:

Therefore:

And finally, the middle part is clearly 4.

And so, the side length must be \(4+4sqrt3\)

Now, a bit of algebra to clean it up, to match what would probably be listed as answer choices:

Thus, \(Area=16sqrt3+24\). And yes, I worked out x2suresh's answer, and the result is the same.

Patrykgb: Your explanation also works; you clearly get the side length correct. The only reason your final answer is not right must be just due to some little computation error. However, that formula with cosine in it shouldn't be necessary, since all GMAT problems must be solvable using "fundamental" math. Also, dude, check out the main forum page; there's a stickied topic that talks about how to use the fun math formatting on this forum. It makes it all look pretty, and it's very easy to lose a little symbol or sign somewhere without it!

tkarthi4u: What formulas are you using? It seems like you're trying to convert to radians.

Vemuri: How did you arrive at your answer?

Enjoy!