The Quadrilateral is JKLM,
let

be the midpoints of JK, KL, LM and JM respectively.
---------------------------------------------------------------------------------------------------------
Given any 2 point P(m,n) and Q(k,l),
the coordinates of the midpoint of the line segment PQ are given by the formula:
,
-------------------------------------------------------------------------------------------------
thus the coordinates of points

are as follows:

------------------------------------------------------------------------------------------------
The distance between any 2 points P(a,b) and Q(c,d) in the coordinate plane, is given by the formula:

------------------------------------------------------------------------------------------------
thus the distances connecting the opposite entrances can be calculated as follows:


Thus the total distance of the paths joining the opposite entrances is
5+5.39 units = 50 m + 53.9 m = 104 m (rounded to the nearest meter)
Answer: 104 m