Inscribed and Circumscribed pentagons

[suedel]

A circle of radius 1, and corresponding circumscribed polygons with the number of sides n=3,4,6, and 8.
A: For each n=3,4,6, and 8, what are the areas of the circumscribed polygons with n sides?
B: Both areas approach a limiting value as n get larger and larger. What number would this be and why?
C: For each n=3,4,6, and 8, 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?

And help would be appreciated.

 

[wjm11]

A circle of radius 1, and corresponding circumscribed polygons with the number of sides n=3,4,6, and 8.
A: For each n=3,4,6, and 8, what are the areas of the circumscribed polygons with n sides?
B: Both areas approach a limiting value as n get larger and larger. What number would this be and why?
C: For each n=3,4,6, and 8, 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?

Compare your areas and perimeters to the area and circumference of the circle. Notice anything? Note that the circumscribed polygon values come closer and closer to the circle values as the number of sides increase.