authors in [@BBCK16] to use results on discrete random planar maps to determine the law of the total intrinsic area of the related growth-fragmentations. On the other hand, it was known that the intrinsic area of the Brownian map cannot be derived as the length of the perimeters of the holes and the height, as for smooth surfaces, since the latter defines a measure that is not locally finite. From the analysis of growth-fragmentations, it has been shown in [@G18] that the intrinsic area of the Brownian map can be written as the integral against the Lebesgue measure of some function of the perimeters of the holes.

Our results in this paper apply to stable surfaces. In particular, Thanks to Theorem \[Theorem area GF\], we retrieve Theorem 3 of Le Gall [@L17], which shows that, in the case of the free Brownian disk with boundary length $x>0$, it holds that $\epsilon^{-2}A(\epsilon)\to x$ almost surely, as $\epsilon\to 0+$ (see ). More generally, we obtain the analogue for other stable disks, with different exponents.

Applying Proposition \[Theorem upper envelope A(t)\] improves the upper bound that was known for the almost sure behaviour of the area of the ball of radius $\epsilon$ around 