The sides of a regular octagon are "s". Find a formula for the distance between the parallel sides of the octagon.

Question

amistre64 · Answer

Hmmm... an 8 sided polygon  If the sides are equal to 1 then we can call it a unit octagon....

what are the interior angles of an octagon equal to?

amistre64 · Answer

360/8 = 45 degrees
45/2 = 22.5 degrees
tan(22.5) degrees = s/2x  ; where x= half the distance across.

2x = s/tan(22.5)
x= s*cot(22.5)/2   ; x is half the distance, so lets multiply both sides by "2" to get the full distance across

d= s*cot(22.5).  Thats the best I can come up with.

the total distance across is equal to

anonymous · Answer

I don't have a problem with using trig to solve it. However this was in an algebra 2 text in a chapter using radicals in equations. the students haven't had trig. But thanks.