# Area and perimeter foliations on spaces of polygons

Aziz El Kacimi Alaoui and Abdellatif Zeggar – GJM, Volume 4, Issue 1 (2019), 18-29.

We describe all families of star-shaped n-polygons in the Euclidean plane with prescribed perimeter and area; they are leaves of a foliation $\mathcal F$ on the space ${\mathcal P}_n^\ast$ of star-shaped polygons. In so doing, we study and record some geometric properties of convex polygons, for instance their inscriptibility in a circle and their regularity in relation with perimeter and area.