Polygon to a Circle
An n-gon inscribed in a circle.
Launch
How does the perimeter of the polygon compare to the circumference of the circle as the number of sides on the polygon increase?
How does the area of the circle compare to the are of the polygon as the number of sides on the polygon increases?
An Octagon inscribed in a circle with a radius of 2.
Question 1
a.
Using your knowledge of angle measures and regular polygons, find the measure of
b.
Next, find the length of segment AJ using trigonometry (round to 3 decimal points).
c.
What is the perimeter of the octagon (round to 3 decimal places)?
d.
Write the formula for the perimeter of an n-gon, where is the number of sides in the n-gon and is the radius of the circle.
An Octagon inscribed in a circle with a radius of 2.
Question 2.
a.
Using the angle found in part 1a, find the measure of segment IJ (also known as the altitude) using trigonometry (round to 3 decimal places).
b.
Find the area of triangle (ABI), rounding to 3 decimal places.
c.
What is the area of the octagon?
d.
Write the formula for the area of an n-gon, where is the number of sides in the n-gon and is the radius of the circle.
Question 3.
How do the area and perimeter formulas for an n-gon help approximate the area and circumference of a circle?