If the nanagon ( 9 sides ) has a length of m inches, then determine the length of the apothem, a

Assuming it is a regular nangon, and m is the length of one of its sides, then consider one

of the triangles. It will be isosceles with the base angles 70° each (easy to figure out)

The apothem will form a right angled triangle with base of m/2 and height h
tan 70° = h/(m/2)
h = (m/2)tan70°