A1. From eight equal isosceles right triangles, we form a regular octagon with an octagonal hole, as shown in the figure. The side length of the regular octagon is $1 \mathrm{~cm}$. How many centimeters is the side length of the octagonal hole?
(A) $\frac{\sqrt{2}}{2}$
(B) $\frac{1}{2}$
(C) $2-\sqrt{2}$
(D) $\sqrt{2}-1$
(E) $\sqrt{3}$

![](https://cdn.mathpix.com/cropped/2024_06_07_58dcb28c79ea4cc315e1g-06.jpg?height=268&width=277&top_left_y=868&top_left_x=1643)
A1. The legs of a certain right-angled triangle are 1 cm long, and its hypotenuse is $\sqrt{2} \mathrm{~cm}$. The side of the octagonal niche is therefore $\sqrt{2}-1 \mathrm{~cm}$.