The regular dodecagon and the blue star inside it both have a side length of 1 unit. What is the area of the star?
The regular dodecagon with side length 1 above is composed of a dark blue star and 12 light blue equilateral triangles with side length 1. The regular dodecagon with side length 1 below is composed of six dark blue squares and 12 light blue equilateral triangles, all of which also have side length 1. Consequently, the star has the same area as the six squares: 6.
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This puzzle originally appeared in Spektrum der Wissenschaft and was reproduced with permission.
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