Question

What is the length of a side of a regular octagon if the major diagonal is 15 meters long?

Answer 1

We can relate the length of the diagonal D with the length of the sides of a regular octagon a with the formula:

`D=a\sqrt[]{4+2\sqrt[]{2}}`

We know that D = 15, so we can find a as:

`\begin{gathered} D=15 \\ a\sqrt[]{4+2\sqrt[]{2}}=15 \\ a=\frac{15}{\sqrt[]{4+2\sqrt[]{2}}} \\ a\approx\frac{15}{\sqrt[]{4+2.8284}} \\ a\approx\frac{15}{\sqrt[]{6.8284}} \\ a\approx(15)/(2.6131) \\ a\approx5.74 \end{gathered}`

NOTE: I did all the calculations without approximating, but as we have irrational numbers, it is always an approximated result.

Answer: the side length is approximately 5.74 meters long.