Calculate the area of the shaded regions. Leave answers in terms of and simplified radicals.
1) Area of the shaded region = ?
2) Area of the shaded region = ?
Calculate the perimeter of each polygon. Leave answers in terms of a trigonometric function.
3) Perimeter of the polygon = ?
4) Perimeter of the polygon = ?
5) Perimeter of the polygon = ?
6) Come up with a general formula for the perimeter of the polygon in terms of . Explain or show your reasoning.
So Many Sides
We can approximate the value of by inscribing an -sided polygon in a circle of radius 1 and calculating the perimeter of the polygon. The formula for the approximation is: . Use this formula to find out how far from these approximations are for the given values of . Round your answers to three decimal places.
11) What value of approximates the value of to the thousandths place?