Question 1077985
Draw a line from a vertex to the opposite side.
By doing that, you make a pair of 30-60-90 
triangles.
Let a side of the original equilateral triangle = {{{ s }}}
So, now the sides of the 30-60-90 triangles are:
{{{ s }}}
{{{ s/2 }}}
{{{ sqrt(3)/2*s }}} ( this one is the line that you drew )
The area of the equilateral triangle is:
{{{ A = (1/2)*s*( sqrt(3)/2*s ) }}}
{{{ A = (1/4)*sqrt(3)*s^2 }}}
{{{ 84 = (1/4)*sqrt(3)*s^2 }}}
{{{ s^2 = 336/sqrt(3) }}}
{{{ s^2 = 336*sqrt(3) / 3 }}}
{{{ s^2 = 112*sqrt(3) }}}
{{{ s = 1.31607*10.583 }}}
{{{ s = 13.928 }}}
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You want the line you drew, so
{{{ sqrt(3)/2*s = (1.732/2)*13.928 }}}
{{{ sqrt(3)/2*s = .866*13.928 }}}
{{{ sqrt(3)/2*s = 12.062 }}} m answer
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check:
{{{ A = (1/2)*13.928*12.062 }}}
{{{ A = 83.9998 }}}
this looks close enough
Definitely get a 2nd opinion on this!!!