Texturing Help for a Noob

Hello, this is my first time using Unity. I am trying to apply a texture to a hexagon that I have created in Blender, but when I drag it onto it, or use material.render, the object has a solid color on it. I do not want to apply the texture in Blender, as I will have different materials that I want the same object to have, but how do I get the full 256x256 texture to appear on the object? Is this something I have to do in Blender?

 

Did you uv unwrap the hexagon? If you want to apply a texture to a model, the model needs to be uv-unwrapped first inorder for the texture to appear correctly.