We have studied a monthly variation of the total sunspot areas during solar cycles 22 to 24 (1986–2016). The ∼6 month smoothed variation (FFT filter technique) of the total sunspot areas shows double peaks (solar maximum) with the ascending phase in each cycle for the periods 1989, 1991, 2000, 2002, 2011, and 2014. We have observed mid-term periodicity (intermediate-term) such as the Rieger-type period (∼120 to ∼190 days), quasi-period (∼200 to ∼380 days), and quasi-biennial period (∼1.20 to ∼3.83 years) of the sunspot areas (total sunspot area, and northern and southern hemisphere of the Sun) for the combined solar cycles 22 to 24; using fast Fourier transform (FFT) and Morlet wavelet transformation (WT) techniques (wavelet power spectra and contour plot). The period ∼1.33 year of the southern hemisphere and total sunspot areas have shown the rotation rates on the basis of the convection zone. The quasi-annual period ∼356 days is observed as an important period for the total sunspot area and the southern hemisphere and are absent in the northern hemisphere of the Sun. The periodicities of the total sunspot areas, and southern and northern hemisphere constitute the fifth, sixth and seventh subharmonic of the solar synodic rotation of ∼27 days in the range of the Rieger-type periodicity. The 24th subharmonic of the solar synodic rotation of ∼27 days is highly significant in the total sunspot area and the southern hemisphere of the Sun during the period of our study (1986–2016).