Move a circle along the broken line (from $A_1$ to $A_n$) with radius $1$ such that it's center always lie on the broken lie. Area of the trace of a circle is equal to $2(A_1A_2+A_2A_3+...+A_{n-1}A_n)+\pi$. Meanwhile distance from any point of the square to the broken line is less than $1$, so every point of the square belongs to the trace of moving circle, so $2(A_1A_2+A_2A_3+...+A_{n-1}A_n)+\pi\ge2500$

WolfusA wrote: Move a circle along the broken line (from $A_1$ to $A_n$) with radius $1$ such that it's center always lie on the broken lie. Area of the trace of a circle is equal to $2(A_1A_2+A_2A_3+...+A_{n-1}A_n)+\pi$. Meanwhile distance from any point of the square to the broken line is less than $1$, so every point of the square belongs to the trace of moving circle, so $2(A_1A_2+A_2A_3+...+A_{n-1}A_n)+\pi\ge2500$ Perhaps you mean perimeter?

No, I mean the area of a figure, that looks like "shade" after moving a circle with radius 1 along the broken line, such that center of circle is moved along the line.