PUMaC 2024 · 几何（B 组） · 第 2 题

PUMaC 2024 — Geometry (Division B) — Problem 2

Let ABCDE be a fixed regular pentagon of side length 1. An equilateral triangle △ P QR with side length 1 is initially placed with P at A , Q at B , and R outside the pentagon. The triangle then rolls without slipping around the perimeter of pentagon until it comes back to its starting point. The total area covered by any part of the triangle during its journey can be √ a b + cπ written as for positive integers a, b, c, d with b square-free and gcd( a, c, d ) = 1. Find d a + b + c + d .

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