Fan of cards

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.

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

Solution by Stéphane Bernard.

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