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#73 Square dance
Set by Sam Hartburn
If you arrange five square tiles, each with side length 1, in a bigger square as shown, what proportion of the area of the square do the tiles use (to three decimal places)?
One of the tiles is rotated by 45 degrees and all five are arranged inside a smaller square as shown. What is this square’s area? What proportion of that area do the tiles use?
Ten tiles in a 4-by-4 square use up 10/16 = 0.625 of the area. But with four of them rotated by 45 degrees, they fit in…
Article amended on 6 June 2025
The third diagram has been corrected.
