$ABCDEFG$ is a convex polygon with area 1. Points $X,Y,Z,U,V$ are arbitrary points on $AB, BC, CD, EF, FG$. Let $M, I, N, K, S$ be the midpoints of $EZ, BU, AV, FX, TE$. Find the largest and smallest possible values of the area of $AKBSCMDEIFNG$.
Source: Israeli Oral Olympiad #1
Tags: geometry
$ABCDEFG$ is a convex polygon with area 1. Points $X,Y,Z,U,V$ are arbitrary points on $AB, BC, CD, EF, FG$. Let $M, I, N, K, S$ be the midpoints of $EZ, BU, AV, FX, TE$. Find the largest and smallest possible values of the area of $AKBSCMDEIFNG$.