Comparing Areas - 3
Consider a regular pentagon. Connect up the alternate sides to obtain a star.
Which is larger, the yellow area or the blue area?
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1 solution
Is there a way of comparing the areas without having to do all of that calculation? It's pretty clear that the blue area is much smaller than the yellow area, so at least the question is easy to answer.
I'm not sure what your calculations say. It seems like you want S 1 S 2 = 2 5 − 1 , but in the next line you say that 2 S 2 + S 1 = 3 S 1 implying that S 2 = S 1 .
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Tanks for your remark. I've corrected my solution.
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I believe that's correct. Thanks for fixing it. Great solution.
I didn't bother calculating the area, and I'm surprised that there's such a nice relationship there. I might post a problem about that.