Regular Octagon Inscribed Inside of a Square

• Sep 10th 2012, 03:48 PM
Seshiru
Regular Octagon Inscribed Inside of a Square
Normally I wouldn't do this, as I derive a certain satisfaction from doing my own work, but I'm growing desperate. This assignment is due tomorrow and the clock is ticking. I thank you all in advance for any help given - it is always appreciated.

A regular octagon is inscribed inside of a square. The length of each side of the square is 8 cm.http://mathcentral.uregina.ca/QQ/database/QQ.09.06/richard1.1.gif This image is quite similar, disregarding the numbers given.

1) What is the exact length of a side of the octagon? Write your answer in simplest radical form.

2) What is the exact area of the octagon? Again, in simplest radical form.

3) To the nearest hundredth, what is the length of a side of the octagon in centimeters?

4) To the nearest hundredth, what is the area of the octagon in square centimeters?

I've gotten as far as determining that the triangles are 45, 45, 90 triangles, and the sides thus represent x, x, x * sqrt(2). Beyond that, I have no idea how to approach the problem. I didn't immediately resort to the internet, I've tried other sources and yes, even my own knowledge. Again, thanks in advance for your help.
• Sep 10th 2012, 04:32 PM
MaxJasper
Re: Regular Octagon Inscribed Inside of a Square
side = $\frac{8}{1+\sqrt{2}}$

are = $64-\frac{64}{\left(1+\sqrt{2}\right)^2}$
• Sep 10th 2012, 04:37 PM
Seshiru
Re: Regular Octagon Inscribed Inside of a Square
Max, do you mind showing me a bit as to how you got your answer?
• Sep 10th 2012, 04:43 PM
MaxJasper
Re: Regular Octagon Inscribed Inside of a Square
a = side of octa

8 cm = 2*[a*cos(45)]+a find a =....
• Sep 10th 2012, 04:53 PM
HallsofIvy
Re: Regular Octagon Inscribed Inside of a Square
You said, "This assignment is due tomorrow and the clock is ticking". Are you saying that you want to get credit for work you have not done? Max Jastper has given you the answer and a hint toward that answer. If you want to take credit for it, the you get that answer.

(Why do you tell us "each side of the square is 8" and link to a picture showing length of each side to be 27?)
• Sep 10th 2012, 05:14 PM
Seshiru
Re: Regular Octagon Inscribed Inside of a Square
I clearly said in my post to disregard the numbers given. I simply asked for help, because you know, this is a forum dedicated for help related to mathematics. If you think I'm the only person on this forum seeking guidance for work that was/will be checked or graded, then you are a fool. If you don't wish to help me, then fine, don't help. This forum is here for a reason. Not everybody knows the answer to every question asked.