Question 985413
That triangle is composed of two 30-60-90 special triangles.


{{{a^2+3^2=6^2}}}
{{{a^2=36-9}}}
{{{a^2=27}}}
{{{a=3sqrt(3)}}}
The equilateral triangle has area, before the circular cut, of {{{(1/2)6*3sqrt(3)=9sqrt(3)}}}.


Cut out the circular piece from the interior,
{{{9sqrt(3)-pi*2^2}}}
{{{highlight(9sqrt(3)-4pi)}}}