Question 838479: I feel so lost and hope I'm doing at least some of this right, can someone show me where I am messing up?
Consider a circle of radius 1, and corresponding circumscribed polygons with the number of sides n = 3, 4, and 6. Drawing a diagram will be extremely helpful.
A: For each n = 3, 4, and 6 what are the areas of the circumscribed polygons with n sides? You must show your work.
B: Both areas approach a limiting value as n gets larger and larger. What number would this be and why?
C: For each n = 3, 4, and 6 what are the perimeters of the circumscribed polygons with n sides? Show your work.
D: The perimeter approaches a limiting value as n gets larger and larger. What number would this be and why?
This is what I have so far:
A:
3 area of circumscribed polygon with n sides is 1/2AP=1/2(1)(6 sqrt3)= 3 sqrt3~ 5.2
4 area of circumscribed polygon with n sides is 2x2=4
6 area of circumscribed polygon with n sides is 1/2AP = 1/2(1)(12/sqrt3)=6/sqrt3~3.5
B:
Area approaches the area of the circle of radius one: π
C:
3 Perimeter of circumscribed polygon with n sides is 2sqrt3 so 6sqrt3 ~ 10.4
4 each side has length 2, so 8
6 each side has length 2/sqrt3 1 so 12/sqrt3~6.9
D:
The area approaches the circumference of the circle of radius one: 2π
Any help would be very much appreciated!
Answer by edjones(8007)   (Show Source):
You can put this solution on YOUR website! A=nr^2*tan(pi/n) from http://www.efunda.com/math/areas/CircumscribePolygonGen.cfm
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P=2nr*tan(pi/n) from the same source.
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B and C are correct.
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Ed
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