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The genealogical structure of self-similar growth-fragmentations can bedescribed in terms of a branching random walk. The so-called intrinsic area$\mathrm{A}$ arises in this setting as the terminal value of a remarkableadditive martingale. Motivated by connections with some models of random planargeometry, the purpose of this work is to investigate the effect of conditioninga self-similar growth-fragmentation on its intrinsic area. The distribution of$\mathrm{A}$ satisfies a useful smoothing transform which enables us toestablish the existence of a regular density $a$ and to determine theasymptotic behavior of $a(r)$ as $r\to \infty$ (this can be seen as a localversion of Kesten-Grincevicius-Goldie theorem's for random affine fixed pointequations in a particular setting). In turn, this yields a family ofmartingales from which the formal conditioning on $\mathrm{A}=r$ can berealized by probability tilting. We point at a limit theorem for theconditional distribution given $\mathrm{A}=r$ as $r\to \infty$, and alsoobserve that such conditioning still makes sense under the so-called canonicalmeasure for which the growth-fragmentation starts from $0$

On conditioning a self-similar growth-fragmentation by its intrinsic area