Question

For this exercise, consider a circle of radius 1, and corresponding circumscribed polygons with the number of sides n = 3, 4, 6, and 8. Drawing a diagram will be extremely helpful.

A: For each n = 3, 4, 6 and 8, what are the areas of the circumscribed polygons with n sides?

Answer 1

for this part of the question I have to use the formula:
A= 1/2ap
where a means apothem and p is perimeter

Answer 2

when YOU draw the diagram you should see that the n sides generate n triangles

and thus subtend n angles of measure 2π / n. These n triangles have sides of

radius , radius , 2 radius sin (π / n ), and height of radius cos (π/n).

Thus area of each is radius squared sin (π / n ) cos (π / n )..SORRY , these are inscribed .

area of each is ' radius tan (π/n) radius ' , so total area is

" n [ radius squared ] tan ( π / n ) "..you can finish this i hope :)

Answer 3

this is what the first figure is suppose to look like.
@ashna i do not understand the sin and cos or tan cause we haven't used them or went over them in class. so there must be a different way. i am really confused.

Answer 4

@smashinsam00 .. Am really sorry but i know this sum by this method ONLY .. hope some one else might help !

Answer 5

@ashna thanks anyway. i can attach the assignment if you want to check it out to see if you understand it

Answer 6

okay i'll try :)

Answer 7

@ashna here is the attachment. hope u have word.

Answer 8

@smashinsam00 am really really sorry .. i dont know this sum other than the method i said .. hope @UnkleRhaukus can help :)

Answer 9

for n=3