Expert: Paul Klarreich - 10/12/2006

Question
Hi,

I need to figure out what size socket to buy for a hard to reach hexagonal nut on my car...
One side = 18mm

Given a the length of one side of a hexagon  , what is the formula for figuring the distance between any two parallel sides?

Thanks,


Answer
Jean Asks in Category Advanced Math ...
 
Subject:  math / geometry
Question:  Hi,

I need to figure out what size socket to buy for a hard to reach hexagonal nut on my car...
One side = 18mm

Given a the length of one side of a hexagon  , what is the formula for figuring the distance between any two parallel sides?

Thanks,
..................................................
Hi Jean,

Your hexagon can be made from six equilateral triangles, each with a side equal to 18.  To get the distance between opposite side, get the distance from the center to the base, which is the altitude of the triangle, then double it.

The altitude is half one side times sqrt(3).  In your case, that is 18/2 times sqrt(3).
Doubling that gives  18 sqrt(3), about  18(1.73).  You can do the rest.