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.