Which statement is true? The law of equal areas suggests that the imaginary line connecting the Sun to a planet sweeps out equal areas, but in a faster time period the closer the planet is to the Sun. The law of equal areas suggests that the imaginary line connecting the Sun to a planet sweeps out equal areas, but in a shorter time period the closer the planet is to the Sun. The law of equal areas suggests that the imaginary line connecting the Sun to a planet sweeps out equal areas in equal amounts of time. The law of equal areas suggests that the imaginary line connecting the Sun to a planet sweeps out different amounts of space in equal amounts of time.