We could use the Model class and render in the Draw method as described in the XNA documentation examples, but lets speed things up and just use the model animator to view it (even though it is not animated).
   // Add this as a member variable
   ModelAnimator ground;

    // Add this in LoadGraphicsContent
    Model groundModel = content.Load<Model>("flat");
    ground = new ModelAnimator(this, groundModel);
    foreach (ModelMesh mesh in groundModel.Meshes)
    {
        foreach (BasicEffect effect in mesh.Effects)
        {
            effect.View = view;
            effect.Projection = projection;
        }
    }
    ground.World =  Matrix.CreateScale(10, 1, 10);