<p>Name: Samantha Nail</p><p>Date: 8/3/12</p><p>Type your response to of the questions below. Then save this document including your last name as part of the document name. </p><p>Week Seven Practical Problem. Read section 7.4 of the chapter 7 PDF for assistance.</p><p>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.</p><p>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 180°.</p><p>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. </p><p>Similarly, an inscribed polygon is surrounded by a circle sharing the same center and goes through each vertex of the polygon. </p><p>A sample of inscribed and circumscribed pentagons is shown below:</p><p>Questions</p><p>For this exercise, consider a circle of radius 1, and corresponding circumscribed polygons with the number of sides n = 3, 4, 6, and 8. Drawing a diagram will be extremely helpful.</p><p>A: For each n = 3, 4, 6 and 8, 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</p><p>3</p><p>4</p><p>6</p><p>B: Both areas approach a limiting value as n gets larger and larger. What number would this be and why? </p><p>C: For each n = 3, 4, 6 and 8, what are the perimeters of the circumscribed polygons with n sides? Show your work.</p><p>Perimeter of circumscribed polygon with n n sides</p><p>3</p><p>4</p><p>6</p><p>D: The perimeter approaches a limiting value as n gets larger and larger. What number would this be and why?</p>