1. An irregular pentagon
2. Interesting question... That depends on the conditions. Even though the left path 'appears to have vegetation', does the that mean the right path has no vegetation at all? Maybe it's a road through a town with little trees (and all the lights are off because it's night-time and although I know it's there because I have a map).
The left path may have bushes and grass and weeds, but may not have trees for shade which would be needed depending on the distance to be travelled and weather. Vegetation also means life (even if there appears to be none) such as snakes, insects, birds and mammals, depending on where I am. It might also mean water, but both paths maybe be through a desert in which case I would pick the left path over the right because water can be extracted from the plants, and maybe I'm hallucinating about my destination being there because I'm so dehydrated.
Or maybe I need to go through a tunnel or go around it and I'm thirsty because I'm in a race or I'm just running for some unknown reason, which is why I'm thirsty. The tunnel is empty and you can't see any birds, bugs or people on the left path. I pick the right path just because I like this scenario better.