N coloured rectangular cards are arranged with a common vertex and common angle α between cards. If a single card has perimeter P, what is the perimeter of the coloured region, in terms of N, P, and α?

Extra condition: N and α are such that at least two edges of the bottom card are visible.

Solution

The perimeter is P(1+(N-1)tan(α)(1-tan(α/2))/2).

N coloured rectangular cards are arranged with a common vertex and common angle α between cards. If a single card has perimeter P, what is the perimeter of the coloured region, in terms of N, P, and α? https://t.co/xsxtT3pWqf By @MarshallWBuck pic.twitter.com/YDCiRjhjlQ

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