If you draw a line from G to H, the quadrilateral becomes two issosolies triangles.
Use the pythagorean theorem to solve for GH using right triangle GHW. GH=sqrt(2).
Because GHW is a right issosolies triangle, angles WGH and WHG are 45 degrees. 105-45=60 so GHB is an equlateral triangle and GH=HB=GB=sqrt(2).
The perimiter is 1+1+sqrt(2)+sqrt(2)=2+2sqrt(2) or ~4.8