Overhang: 广
The 广 component, called まだれ, sits over the left side and suggests a roof or shelter. That fits offices in 府 and 庁; in 底 (“bottom”), the connection is less direct, so treat the shared shape as a clue, not a full explanation.
府 and 底 each have 8 strokes; 庁 has 5. Keep the wide 广 roof clear before adding the lower part.