TITLE: About the ratio of the areas of a convex pentagon and the inner pentagon made by the five diagonals
QUESTION [34 upvotes]: Question : Letting $S{^\prime}$ be the area of the inner pentagon made by the five diagonals of a convex pentagon whose area is $S$, then find the max of $\frac{S^\prime}{S}$.
                  

I've been interested in this simple question. It seems that a regular pentagon and its affine images would give the max, but I'm facing difficulty.
Remark : This question has been asked previously on math.SE without receiving any answers.

REPLY [4 votes]: A complete solution is available at https://arxiv.org/abs/1812.07682
On the polygon determined by the short diagonals of a convex polygon,
Jacqueline Cho, Dan Ismailescu, Yiwon Kim, Andrew Woojong Lee