It is shown that exciton and multi-exciton emission lines ("spectral barcode") of a quantum dot conceal nontrivial structural information on the shape and size of the dot, information which can be uncovered by comparison with atomistic many-body theory. Application to the newly-established strain-free GaAs quantum dots grown via "droplet epitaxy" onto AlGaAs matrix reveal the shape and size as "seen" by spectroscopy. The results show that the previously determined dot height (∼ 14 nm) as "seen" by cross-sectional scanning tunneling microscopy (XSTM) could not possibly be consistent with the excitonic signature (1.7-1.9 eV), as the latter must reflect a 1-4 nm tall dot. Multi-exciton "barcode" and fine structure spitting suggest GaAs/AlGaAs dots are in Gaussianshape in agreement with XSTM measurement. Both spectroscopy and XSTM measurements were done on GaAs dots capped by the Al0.3Ga0.7As barrier layer. The fact that XSTM sees tall dots and spectroscopy sees short dots is thus not because the dot change its height in one experiment relative to the other, but because different dots must have been used. This was uncovered by theoretical simulation of the experiment showing that the two experiments could not possibly correspond to the same dot.