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

Algebra ->  Algebra  -> Triangles -> SOLUTION: Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 6-inch apothem A = sq. in      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 368864: Find the area of an equilateral triangle (regular 3-gon) with the given measurement.
6-inch apothem
A = sq. in
Answer by edjones(7569) About Me  (Show Source):
You can put this solution on YOUR website!
There are now two 30-60-90 triangles with side ratios of 1:sqrt(3):2
Let b=base
b/1=6/sqrt(3) Proportion
A=0.5*6*(6/sqrt(3))
=18/sqrt(3)
=18/sqrt(3) * sqrt(3)/sqrt(3) Rationalize the denominator.
=18sqrt(3)/3
=6sqrt(3)
.
Ed