Question 1061957
How high is the equilateral triangle?  
Base is S and the length of the other two of its sides also S each.  Pythagorean Theorem formula will help; imagine cutting the triangle into two parts along the altitude.


{{{S^2=((1/2)S)^2+a^2}}}, using "a" for the altitude length.
{{{a^2=S^2-S^2/4}}}
{{{a^2=4S^2/4-S^2/4}}}
{{{a^2=3S^2/4}}}
{{{highlight_green(a=S*sqrt(3)/2)}}}



Area of the whole rectangle:
{{{S*2S}}}
{{{highlight(2S^2)}}}


Fraction of the area which is uncovered:
{{{(totalArea-coveredArea)/totalArea}}}
-
{{{(2S^2-(S^2+(1/2)S*a))/(2S^2)}}}



Substitute for a:


{{{(2S^2-(S^2+(1/2)S(S/2)sqrt(3)))/(2S^2)}}}

The simplification algebra steps are not shown here, but final result should be {{{highlight((4-sqrt(3))/8)}}}.