Which Athenian institution was responsible for overseeing the administration after their term as archons?

The correct answer is the Areopagus, which served as a key institution in the governance of ancient Athens, particularly after the term of archons. Historically, the Areopagus was composed of former archons, and its primary responsibility was to supervise and oversee various aspects of civic administration and judicial matters. This council was a powerful body that ensured the continuity and experience of governance, as its members were individuals who had already held significant political office.

The Areopagus also played a crucial role in maintaining laws and traditions and had the authority to scrutinize the actions of the archons, which helped to provide a check on their power. Its function extended to handling serious criminal cases and overseeing moral conduct within the city-state, solidifying its position in Athenian political life.

In contrast, the other institutions mentioned have different roles: the Heliaia was a popular court system where citizens could serve as jurors, the Boule functioned as a council of representatives that proposed legislation and managed day-to-day governance, and the Ekklesia was the assembly where citizens gathered to debate and vote on important decisions. Thus, while each institution had its unique responsibilities, the Areopagus specifically focused on oversight and administration after the archons' term,