Posted by Nick on Thursday, February 28, 2013 at 9:01pm.
If I recall, apothem is the distance from the centre to the midpoint of a side
so look at one of the equal 5 isosceles triangles.
the central angles are 360/5 or 72° each, making the base angles 54°.
let the base be length x
then
tan 54° = apoth/(x/2)
apothem = (1/2) base x tan 54°
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