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HMMT 十一月 2017 · 冲刺赛 · 第 8 题

HMMT November 2017 — Guts Round — Problem 8

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 3 ] Regular octagon CHILDREN has area 1. Find the area of quadrilateral LIN E .
解析
  1. [ 3 ] Regular octagon CHILDREN has area 1. Determine the area of quadrilateral LIN E . Proposed by: Yuan Yao 1 Answer: 2 √ √ 2 1 2 Suppose that the side length CH = 2 a , then the area of the octagon is ((2 + 2) a ) − 4 · a = 2 √ √ √ √ 2 2 (4 + 4 2) a , and the area of LIN E is ( 2 a )((2 + 2) a ) = (2 + 2 2) a , which is exactly one-half of 1 the area of the octagon. Therefore the area of LIN E is . 2