at the age of
意思是”在...年代（時(shí)期）",比如：在中世紀(jì)時(shí)期——at the age of medieval times.
另外一個(gè)意思是”在...歲時(shí)",比如：在5歲時(shí)——at the age of five
at a age of
意思是“在...年齡時(shí)“,一般作為敘述,或比較.
比如說,你再給一個(gè)朋友聊天,你突然回憶大發(fā),談到：在我兒子這么大的時(shí)候,我都會(huì)放牛了.
這個(gè)時(shí)候就用“at a age of“,例句：I already learned how to wrangle cattles at a age of my son.
若還有不明白,可以百度HI我.