Problem 45408. Yoonir - 03

Created by Asif Newaz

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Find the area of a seven-pointed star inscribed in a circle of radius r.

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Last Solution submitted on Jun 13, 2025

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William on 5 Apr 2020

Hi Asif,
I'm puzzled. Now 2 people have submitted solutions that agree with the test suite, but the test suite seems wrong to me! Looking at all 3 'yoonir' problems for a radius of 10 units:
Program Points test_suite my_calc
yoonir_02 5 112.27 112.26
yoonir_04 6 173.20 173.21
yoonir_06 7 108.34 210.17
How would it be possible that in going from a 6 pointed star to a 7 pointed star, the area drops from 173.2 to 108.3?

Asif Newaz on 7 Apr 2020

hello William,

in the figure, the available area inside the polygon of a 7-pointed star has actually decreased compared to 6-pointed star .isn't it?

Asif Newaz on 7 Apr 2020

https://i.pinimg.com/474x/27/ce/d6/27ced6447ff40b38ae3d5784b30936a9.jpg

William on 7 Apr 2020

Gosh, that seems to be right! I thought my solution was good for all N, but I can see from that figure that it's not. Thanks for the tip.

William on 8 Apr 2020

Asif,
I have discovered something! While there is just one way to draw a five-pointed star or a six-pointed star, there are actually two ways to draw a seven-pointed star. One of them has an area much larger than the other.

Asif Newaz on 9 Apr 2020

yes i saw that later on utube..didn't know that before

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Problem 45408. Yoonir - 03

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Problem 45408. Yoonir - 03

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