1. A pentagram is inscribed in a circle of radius 1.
Find all of the lengths and all of the angles. Find the area and the perimeter of the pentagon. Find the area and the perimeter of the five pointed star inside the pentagon.
2. The 8 pointed star is inscribed in a circle of radius 1.
Find all of the lengths and all of the angles. Find the area and the perimeter of the star.
3. The 12 pointed star is inscribed in a circle of radius 1.
Find all of the lengths and all of the angles. Find the area and the perimeter of the star.
4. An n pointed star is formed by placing n points equally spaced on a circle the n points are joined with n lines which are all equally long. If the lines join each point with the point which is k points away then we refer to the star as the {n/k} star. The pentagon is the {5/1} star. The nonconvex 5 pointed star is the {5/2} star. The star in 2 is the {8/3} star, and the star in 3 is the {12/5} star. Find general formulas for the area and perimeter of an {n/k} star which is inscribed in a cirlce of radius r. Your group will receive extra credit if you can find more than one formula for the area or the perimeter. If you should find more than one formula for the area or the perimeter, your group will receive still more extra credit if you can show that the formulas are the same by the use of trigonometric identities.