In a convex $12$-gon, all angles are equal. It is known that the lengths of some $10$ of its sides are equal to $1$, and the length of one more equals $2$. What can be the area of this $12$-gon?
Source: Moscow mathematic olympiad 2022, Day 2 P11.3
Tags: geometry
In a convex $12$-gon, all angles are equal. It is known that the lengths of some $10$ of its sides are equal to $1$, and the length of one more equals $2$. What can be the area of this $12$-gon?