Let $ABCDE$ be an equiangular convex pentagon with perimeter $2$. The pairwise intersections of the lines that extend the sides of the pentagon determine a five-pointed star. Let $s$ be the sum of the lengths of the ten segments forming the 'points' of this star (i.e., the sum of the lengths of the two equal sides of each of the five isosceles triangles whose bases are the sides of the pentagon and whose vertices are the points of the star). What is the value of $s$?