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HMMT 二月 2022 · 冲刺赛 · 第 1 题

HMMT February 2022 — Guts Round — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [5] A regular 2022-gon has perimeter 6 . 28. To the nearest positive integer, compute the area of the 2022-gon.
解析
  1. [5] A regular 2022-gon has perimeter 6 . 28. To the nearest positive integer, compute the area of the 2022-gon. Proposed by: Akash Das Answer: 3 Solution: Note that the area of a regular 2022-gon is approximately equal to the area of its circum- circle, and the perimeter of a regular 2022-gon approximately equals the perimeter of its circumcircle. Since the perimeter is 6 . 28 ≈ 2 π, the circumradius R ≈ 1, so the area of the 2022-gon is approximately 2 R π ≈ π ≈ 3.