An assembly is provided for an aircraft propulsion system. This assembly includes a variable area inlet, and the variable area inlet includes an inlet structure, an inlet lip, an inlet orifice and an inlet passage extending within the variable area inlet from the inlet orifice. The inlet lip is configured to pivot about a pivot axis between a first position and a second position. The inlet orifice is formed by and between the inlet structure and the inlet lip. The inlet orifice has a first area when the inlet lip is in the first position. The inlet orifice has a second area when the inlet lip is in the second position. The second area is different than the first area.