Expert: Vishwas K Hajirnis - 10/10/2006

Question
I have to make a picture frame in an irregular octogon shape. It has to be 15" wide and 40" long. The top and bottom 3 sides will be equal. How do I calculate all the sides?

Answer
As I understand it, not only the bottom 3 sides but even the top 3 sides will also be equal. Only sides which will be longer ( by 40"-15"=25" ) will be the 2 sides along the 40" sides.
So for calculation the remaining sides of the octagon we need to calculate the sides of a regular octagon that can be fitted in a 15" by 15" square frame. So assuming we have a square frame of 15" by 15", the radius of the inscribed circle must be 15"/2=7.5".
If each side is 'a' and the radius of the inscribed circle is 'r', then we have a formula

a = 2r(sqrt[2]-1)

Substituting r=7.5", we get
a=2*7.5*(sqrt(2)-1)
a=6.213203436"
So each of the 3 sides ( actually from symmetry 6 sides) will be approximately 6.31" and the remaining 2 sides ( along the 40" borders ) will be 6.21"+25"=31.21"