IM Geo.4.11 Lesson: Approximating Pi

Calculate the area of the shaded regions.
Calculate the area of the shaded regions.
The applet below shows a regular n-sided polygon inscribed in a circle.
Come up with a general formula for the perimeter of the polygon in terms of [math]n[/math].  Explain or show your reasoning.
Let's use the expression you came up with to approximate the value of π.
How close is the approximation when [math]n=6[/math]?[br]
How close is the approximation when [math]n=10[/math]?[br]
How close is the approximation when [math]n=20[/math]?[br]
How close is the approximation when [math]n=50[/math]?[br]
What value of [math]n[/math] approximates the value of [math]\pi[/math] to the thousandths place?
Describe how to find the area of a regular [math]n[/math]-gon with side length [math]s[/math]. Then write an expression that will give the area.
Luk

Information: IM Geo.4.11 Lesson: Approximating Pi