The N-S asymmetry (the north-south hemispheric asymmetry) of sunspot areas for each of the cycles 7-24 have been investigated, and a trend of a long-term characteristic timescale of about eight cycles is inferred, which is confirmed again by studying the fitted lines of the yearly values of the N-S asymmetry of sunspot numbers and sunspot group numbers at solar cycle 24. Then, a periodic behavior of about 12 solar cycles is found in the cumulative counts of yearly sunspot areas for each of the cycles 7-24. Nevertheless, the cumulative counts of sunspot numbers and sunspot group numbers for cycle 24 have different behaviors. Moreover, the dominant hemispheres for cycles 7-23 show a trend of a long-term characteristic timescale of about 12 cycles. However, we cannot determine the dominant hemisphere of cycle 24, as these three parameters give different results for the dominant hemisphere. Cycle 24 is a particular solar activity cycle, as sunspot areas suggest a long characteristic timescale of about 12-cycle length, while sunspot numbers and sunspot group numbers support an eight-cycle period of the N-S asymmetry.