Originally posted by wolfgang59 Correct but you have assumed the reader knows ratios of the sides of a 30, 60, 90 triangle.

I thought a neater idea was to spot that the described triangle is a third of an equilateral triangle of side 12.

So using your shortcut we have area of equilateral triangle is
0.5 * 12 * 6sqrt3 = 36sqrt3

Therefore isoceles is 12sqrt3

I said it was easy!!

Really elegant. Also...it can be viewed as being equal to the area of an equilateral triangle of side 12/(sqrt(3)).
The two halves of this equilateral triangle having been juxtaposed to form the given isosceles triangle with vertex angle 120 deg...