Well,i doubt whether v can prove if 45-45-90 is possible here..

A is clearly insufficient.

stmnt B=

let midpt of BC be - x

Hence, BX=BC=2 ----- GIVEN

Now,as triangle EXC is right angled,and as we know the 2 given sides of that triangle we can find Side EX...

Now,let Y be point on side DC...if we observe EY has length similar to that of XC..We can clearly say that EY=XC=2..

Therefore, as we know that triangle EYC is right angled and as we know 2 sides,by using pythagoras,we can find the remaining side..

hence we have found the values of all sides,we can find its area..

_________________

ITS NOT OVER , UNTIL I WIN ! I CAN, AND I WILL .PERIOD.