Posted by **Nick** on Thursday, February 28, 2013 at 9:01pm.

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

- Geometry -
**Reiny**, Thursday, February 28, 2013 at 10:15pm
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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