HMMT 二月 2016 · 几何 · 第 1 题
HMMT February 2016 — Geometry — Problem 1
题目详情
英文原题
- Dodecagon QW ART ZSP HIN X has all side lengths equal to 2, is not self-intersecting (in particular,
° °
the twelve vertices are all distinct), and moreover each interior angle is either 90 or 270 . What areall possible values of the area of 4 SIX ?
解析
英文解析
- Dodecagon QW ART ZSP HIN X has all side lengths equal to 2, is not self-intersecting (in particular,
° °
the twelve vertices are all distinct), and moreover each interior angle is either 90 or 270 . What areall possible values of the area of 4 SIX ?
Proposed by: Evan Chen
Answer: 2 , 6
The dodecagon has to be a ”plus shape” of area 20, then just try the three non-congruent possibilities.