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

Area of a triangle equal base time height divide 2

in this case the heght mean the apothem 

hope you know that an equilateral triangle has every angles equal 60 degrees and every sides length are congruent 

and the apothem is bisector 

so you can writing sin60 = apothem divide hypotenuse so 

sqrt3 /2 = apothem / side length 

sqrt3 /2 = 6/side length

side length *sqrt3 = 12 

side  length = 12 /sqrt3 

side length = 12sqrt3 /3

in this case area = (12sqrt3 /3 *6)/2 = (12sqrt3 /3 *3) = 12sqrt3 in^2

hope this will you