SOLUTION: The length of a piece of wire is 8 inches. It is then formed into a regular hexadecagon (polygon of 16 sides). What is the area of the polygon?

Question 1077071: The length of a piece of wire is 8 inches. It is then formed into a regular hexadecagon (polygon of 16 sides). What is the area of the polygon?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39799) (Show Source): You can put this solution on YOUR website!
The center and any two neighboring vertices of the polygon form an isosceles triangle, base side of length inch. Apex angle measure degrees; each base angle degree each.

Length h, of either of the equal sides of one of these triangles:

The ALTITUDE of one of these isosceles triangles:
a, the altitude

--------the altitude.
NOT finished.
Simplify this and then calculate the area for the whole polygon of 16 sides.

Area, -----substitute for a, and simplify this expression.
Answer by MathTherapy(10810) (Show Source): You can put this solution on YOUR website!

The length of a piece of wire is 8 inches. It is then formed into a regular hexadecagon (polygon of 16 sides). What is the area of the polygon?

Apothem =
Area of one of the hexadecagon's triangles =
Area of hexadecagon:
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