Regular Octagon Made By Cutting Equal Triangles Out From The Corners Of A Square

$x^2 = a^2 + a^2$

$x^2 = 2a^2$

$x = \sqrt{2}a$
 

 

$x + 2a = 16$

$\sqrt{2}a + 2a =16$

$\left( \sqrt{2} + 2 \right)a = 16$

$a = \dfrac{16}{\sqrt{2} + 2}$
 

$x = \sqrt{2}\left( \dfrac{16}{\sqrt{2} + 2} \right)$

$x = 6.627 ~ \text{cm}$   ←   answer