A dissection of a polygon $P$
is a partition of $P$ into a finite number of pieces, which can then be rearranged
(via planar translations and rotations) and joined (without overlap) to form a new polygon $P'$.
Say that a polygon $P$ has an *inside-out dissection* (my terminology)
if $P'$ is congruent to $P$, and the perimeter of $P$ becomes interior to $P'$,
and so the perimeter of $P'$ is composed of internal cuts of the dissection of $P$.

I believe every polygon $P$ has an inside-out dissection because (1) $P$ may be triangulated, and (2) every triangle has an inside-out dissection:

One may ask many questions concerning this concept. Here I will confine myself to three:

Q0. Has this notion been explored before, and if so, under what name?

Q1. Is there an inside-out dissection of a generic triangle using fewer than $9$ pieces?

Q2. There is a "$+$" inside-out dissection of any rectangle into $4$ pieces. What is the minimal inside-out dissection of a generic trapezoid?

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