I have to place 8 copies of the following figure
on a piece of paper with a width of $90$ cm.
The question is how should I place the figures in order to use the least amount of paper?
Here is my try (by trial and error) but can it be done any better? (The $x$-coordinate of the right-most point is approximately $91{,}81$.)
It is an exam question from 2019 from the Danish secondary school system. I'm a teacher and the only motivation is that I would like to show the best possible solution for my students.
Here is a much better solution that fits within a $9×8.61$ sheet (with each unit being $10\text{ cm}$). I have good reason to think it is optimal but who knows...
The idea was to pack 4 kites into the left half that has height $9$ and width roughly $4.5$, except that the lower part juts out by a bit to the right while the upper part has leftover space on the right, and then rotate the left half by 180° to get the right half.