Question 973425
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s=side of equilateral triangle, a=apothem=9
The apothem is the longer leg of a 30-60-90 triangle 
with one side of the equilateral triangle as hypotenuse
and one half one side as the shorter leg.  
{{{s^2=(s/2)^2+a^2}}}
{{{s^2=(s^2/4)+9^2}}}
{{{s^2=s^2/4+81}}} Multiply by 4
{{{4s^2=s^2+324}}}
{{{3s^2=324}}}
{{{s^2=108}}}
{{{s=10.39}}}
The side of the equilateral triangle is 10.39.
The base of the right triangle which makes up half of the 
equilateral triangle is 1/2 of a side (1/2)(10.39)=5.195 units
The height of this right triangle is the apothem (9 units)
The area of the right triangle is (1/2)(5.195)(9)=23.4 square units
Since two of these right triangles make up the equilateral triangle,
area of the equilateral triangle is (2)(23.4)=46.8 square units.