Modeling radiative transfer in a 3D cloudy atmosphere is critical to climate projections. A recently developed fast 3D radiation parameterization scheme gains some success in quantifying horizontal radiative transfer through cloud sides using cloud area fraction. Based on 3D Monte Carlo simulations of radiative transfer through an idealized single-layer cloud with Koch-shaped fractal geometry edges, here we show that radiative energy transport through cloud sides correlates more significantly with cloud area fraction than with cloud perimeter length. The results exemplify the importance of accounting for the horizontal radiative energy exchanges between cloud-free and cloudy regions with cloud area fraction. Results from additional sensitivity simulations show that increased cloud vertical extent often enhances cloud-side sunlight leak more significantly than cloud-side sunlight interception. At low sun elevations, cloud-side sunlight interception is enhanced more than cloud-side sunlight leak does with the increase of cloud mass.