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.
IM Geo.4.11 Practice: Approximating Pi
A regular pentagon has side length 7 inches.
What is the perimeter of the pentagon? [br]
What is the area of the pentagon? [br]
[size=150]The expression [math]n\cdot sin\left(\frac{360}{2h}\right)[/math] approximates [math]\pi[/math] by giving the perimeter of a regular polygon inscribed in a circle with radius 1.[br][/size][br]What does [math]n[/math] stand for in the expression? [br]
If there are 60 sides, what is the difference between the perimeter and [math]\pi[/math]? [br]
Technology required. A regular hexagon has side length 2 inches.
What is the perimeter of the hexagon? [br]
What is the area of the hexagon? [br]
An airplane travels 125 miles horizontally during a decrease of 9 miles vertically.
What is the angle of descent?[br]
What is the distance of the plane’s path?[br]
Select [b]all [/b]true 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[/img]
Write 2 equations using sine and 2 equations using cosine based on triangle [math]ABC[/math]. 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[/img]
An equilateral triangle has area of [math]36\sqrt{3}[/math] square units. What is the side length?