Name: Fraley, Meghan

Date:8/16/13

Type your response to of the questions below. Then save this document including your last name as part of the document name.

Week Seven Practical Problem. Read section 7.4 of the chapter 7 PDF for assistance.

In this assignment, you examine a process that links polygons and circles. You will reach some quantitative conclusions about their respective areas and the relationship between the two.

As you know, a regular polygon has sides of equal length and angles that are the same. This confers a high degree of symmetry to these figures. A circle may be thought of as the logical limit of an n-sided polygon as n goes to infinity; the sides become infinitesimally small, and the interior angle between adjacent sides continues toward 180째.

A circumscribed polygon is a regular polygon that surrounds a circle. The radius of the circle is the length of the apothem of the polygon; both share the same center. This means the circle touches the polygon on the inside in the middle of each side of the polygon.

Similarly, an inscribed polygon is surrounded by a circle sharing the same center and goes through each vertex of the polygon.

A sample of inscribed and circumscribed pentagons is shown below:

Questions

For this exercise, 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? Hint: Use. You must show your work.

n Area of circumscribed polygon with n sides 3 4 6
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.
n Perimeter of circumscribed polygon with n sides 3 4 6
D: The perimeter approaches a limiting value as n…