Question 1180055


The internal angles of a regular hexagon is {{{360/6 = 60}}} degrees
 
The diagonals connecting the two edges of opposite sides makes equilateral triangles with apex at the centre.
 
Hence the perpendicular distance would be twice that of the longer side of a 30/60/90 degree triangle with hypothenuse {{{8cm}}}.
 
Using Pythagoras theorem 

{{{d = 2*sqrt(8^2 - 4^2)}}}

 {{{d = 2*sqrt(64 - 16)}}}

{{{d = 2* sqrt(48)}}}

{{{d = 8sqrt(3)}}}

Hence this length would be {{{8sqrt(3)cm}}} exactly, or {{{ 13.9cm}}} approximately