math

The apothem of a regular polygon is the distance from the center to any side.
If the length of the apothem remains constant at 10 inches, the formula for the perimeter of a regular polygon as a function of the number of sides is ( ) ( )( ).
As the regular polygon changes from a pentagon (5 sides) to an octagon (8 sides), what is the approximate average rate of change in the perimeter?

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  1. If the perimeter is p, the area is A = 1/2 ap.

    So, since p = ns, what is the side s of an n-gon?

    The central angle of each of the n isosceles triangles is θ=360/n, so the side is

    s = 20 tan(θ/2)

    Thus, the area is

    A = 1/2 a (ns) = 1/2 (10) (n*20 tan 180/n)
    = 100n tan(180/n)

    You can probably handle the rest, eh?

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