Question
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?
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?
Answers
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?
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?
2+2=1
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