Can you calculate the side length of a regular n-gon given its apothem?
apothem = a
side length=s
#sides = n formula please
2007-01-05 08:22:49 · 2 answers · asked by T-wad 2 in Science & Mathematics ➔ Mathematics
These are all that you have to work with
2007-01-05 08:37:44 · update #1
The apothem and half the side make 2 perpendicular sides of a right triangle, and the hypotenuse is a radius of the n-gon. If there are n sides, the angle between the radius and the apothem is 360/(2n) = 180/n. The half-side is opposite this angle, and the apothem is adjacent, so use tangent. The basic equation will be
(s/2)/a = tan (180/n)
s = 2a tan (180/n)
2007-01-05 09:01:49 · answer #1 · answered by Philo 7 · 0⤊ 0⤋
Start by taking (n - 2) * 180 / (2n) ... the angle at the bottom of the triangle that contains the apothem. Call this angle T.
You can find half the side by taking a / tanT.
So the whole side is 2 (a / tanT).
2007-01-05 08:30:46 · answer #2 · answered by dmb 5 · 1⤊ 0⤋