How do you find the apothem of a regular pentagon? Hexagon?

Answer 1

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°