In area scoring, your score is the sum of two components
- the number of empty points only your stones surround and
- the number of your stones on the board (AXA rules: White adds N-1, where N is the number of handicap stones, so as to not give an advantage to Black for having had more stones on the board before play started)
Area scoring is independent of life and death, even though some rule sets abuse those terms as if they were relevant. Life and death exist on the strategic level. Strategically dead stones should be removed so that only the strategically alive stones remain that then surround empty points that before were not surrounded by either player's stones because typically those empty points were in between strategically alive stones of one player and strategically dead stones of his opponent.
Robert Jasiek has written several notes on Area Scoring.