Devide a Triangle

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I don't understand why you are using different shades of gray there.
But I would think, if you used a texture on the new formed surface, the texture would take care of itself.
I think your problem is with the UV values of your texture.
Are you setting the UV values for the mesh?
What I see looks like something I was getting because I didn't have the UV set right.
I had a grass texture made of random shades of green, and when I used it on my mesh
all I got was a green smear, something like the gray images you show us.
I then set the UV for the mesh and got a nice random grass field look.