Find the area of a triangle given one side and angle and the sum of the other two sides – math.stackexchange.com

I'm stuck in the following problem. I don't remember where I found it, but is kind of an Olympiad problem. Let $ABC$ be a triangle where $a=\sqrt{6}, \hat{A}=\pi/6$ and $b+c=3+\sqrt{3}$. Fin the area ...