We analyze the colors and sizes of 32 quiescent ( UVJ-selected ) galaxies with strong Balmer absorption ( \mbox { EW } ( H \delta ) \geq 4 Å ) at z \sim 0.8 drawn from DR2 of the LEGA-C survey to test the hypothesis that these galaxies experienced compact , central starbursts before quenching . These recently quenched galaxies , usually referred to as post-starburst galaxies , span a wide range of colors and we find a clear correlation between color and half-light radius , such that bluer galaxies are smaller . We build simple toy models to explain this correlation : a normal star-forming disk plus a central , compact starburst component . Bursts with exponential decay timescale of \sim 100 Myr that produce \sim 10 \% to more than 100 % of the pre-existing masses can reproduce the observed correlation . More significant bursts also produce bluer and smaller descendants . Our findings imply that when galaxies shut down star formation rapidly , they generally had experienced compact , starburst events and that the large , observed spread in sizes and colors mostly reflects a variety of burst strengths . Recently quenched galaxies should have younger stellar ages in the centers ; multi-wavelength data with high spatial resolution are required to reveal the age gradient . Highly dissipative processes should be responsible for this type of formation history . While determining the mechanisms for individual galaxies is challenging , some recently quenched galaxies show signs of gravitational interactions , suggesting that mergers are likely an important mechanism in triggering the rapid shut-down of star-formation activities at z \sim 0.8 .