Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 6-inch apothem

Question

Find the area of an equilateral triangle (regular 3-gon) with the given measurement.  6-inch apothem

anonymous · Answer

I've done this problem before, does it show the following...
"Find the area of an equilateral triangle (regular 3-gon) with the given measurement.

6-inch apothem

A = sq. in."?

anonymous · Answer

yes

anonymous · Answer

6-inch apothem, apothem a = 6 
an equilateral triangle has 6 30-60-90 triangles each with the shortest leg being the apothem, length = a = 6 
find hypotenuse of each of the 6 triangles:
angle opposite to a is 30 degrees,
sin 30 = opposite/hypotenuse = a/hyp = 6/hyp
0.5 = 6/hyp
0.5hyp = 6
hyp = 12 inches 
Can you tell me, how to find adjacent of each of the 6 triangles?