An analysis of Lyman series lines arising from hydrogen-like oxygen and neon ions in the coronae of the active RS CVn-type binaries II Peg and IM Peg, observed using the Chandra High Resolution Transmission Grating Spectrograph, shows significant decrements in the Lyα/Lyβ ratios as compared with theoretical predictions and with the same ratios observed in similar active binaries. We interpret these decrements in terms of resonance scattering of line photons out of the line of sight; these observations present the first strong evidence of this effect in active stellar coronae. The net line photon loss implies a nonuniform and asymmetric surface distribution of emitting structures on these stars. Escape probability arguments, together with the observed line ratios and estimates of the emitting plasma density, imply typical line-of-sight sizes of the coronal structures that dominate the X-ray emission of 1010 cm at temperatures of 3 × 106 K and of 108 cm at 107 K. These sizes are an order of magnitude larger than predicted by simple quasi-static coronal loops models but are still very small compared to the several 1011 cm radii of the underlying stars.