Question 456962
From elementary geometry, the 45 degree interior angle is opposite the shortest side with length 2.  This side is adjacent to the 60 degree interior angle.  The other side adjacent to {{{60^o}}} is opposite the largest interior angle ({{{75^o}}}), which we denote by x.  From the sine law, 

{{{x = (2sin75^o)/sin45^o}}}

==>  {{{A = (1/2)absinC = (1/2)*2*((2sin75^o)/sin45^o)*sin60^o = ((2sin75^o)*(sin60^o))/sin45^o) = (3+sqrt(3))/2 }}} = 2.366 square units.