As others have said this looks like uv coordinates are wrong. You want to map the whole texture to the rectangle correct?
Assuming your rendering as triangle strips try implementing the following pseudocode:
vert 1.texcoord = 0,0
vert 2.texcoord = 0,1
vert 3.texcoord = 1,1
vert 4.texcoord = 1,0
If that doesn't work try shifting the coords between the different verts, one combination should work for you.