I believe "der Bauer" can also be translated as "the peasant". Not sure why that translation is marked as incorrect.
I'm not sure about the english meading of peasant. As I understand it, it includes some kind of social position, farm laborers of low social rank. (?)
Whereas farmer (and "Bauer") refers to the profession. the person farming the land.
Peasant is a historical expression for what we now call "farmer", i.e. someone who used to work in agriculture. Incidentally, peasants were usually of low social status, hence its wide-ranged use as a derogatory term, but that is unrelated to the point I am trying to make. Since the historical context of the statement to be translated is undetermined, and considering "peasant" is still very much part of living language, I think it should be accepted as a solution.
I am not sure whether you consider this important, but the Wikipedia article "Peasant" corresponds to the German Wikipedia article "Bauernstand" (peasantry), and Google Translate translates "peasant" as "Bauer".
Well guess I'm the wrong person to judge the english meaning, since there is only one Word for "Bauer" in german.
I can only provide an explanation for the german words.
Bauer ist just the profession. Theres no social rank or group included. It can be a person with a small farm or a really wealthy "Großbauer". Whereas "Bauernstand" is a historical term for a social group and implies a picture of poor people working for the upper class.
But you are right, since we have no context, peasant should be ok.
Bauer can also be used as an insult, but thats off topic.
Actually, there is another similar word to "Bauer", which is "Landwirt". It is a more recent word, and you will sound more educated, using "Landwirt". Usually both mean the same, a person that farms land (crops, cows, and so on). Technically you need a completed education to call yourself "Landwirt". But if you watch the news, both are used synonymous most of the time.