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Elementary Geometry for College St...
Solutions
Elementary Geometry for College St...
In Exercises 17 to 30, use the formula
In a regular dodecagon (12 sides), the approximate ratio of the length of an apothem to the length of a side is 15:8. For a regular dodecagon with an apothem of length 12 ft, find the approximate area.
To find:
The approximate area of a regular dodecagon.
Concept:
1) The perimeter of a regular polygon is given by P = ns, where n is the number of sides and s is the length of any side.
2) The area of a regular dodecagon with apothem a and perimeter P is given by
Calculation:
It is given that the approximate ratio of the length of an apothem to the length of a side is 15:8.
By proportionality constant, a = 15x and s = 8x.
It is also given that the length of the apothem is 12 ft.
Substitute a = 12 in a = 15x.
Substituting x = 0.8 in s = 8x.
s = 8(0.8)
= 6.4 ft
The total number of sides in a regular dodecagon is 12
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