HMMT 十一月 2018 · 冲刺赛 · 第 6 题
HMMT November 2018 — Guts Round — Problem 6
题目详情
- [ 6 ] An equilateral hexagon with side length 1 has interior angles 90 , 120 , 150 , 90 , 120 , 150 in that order. Find its area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HMMT November 2018, November 10, 2018 — GUTS ROUND Organization Team Team ID#
解析
- [ 6 ] An equilateral hexagon with side length 1 has interior angles 90 , 120 , 150 , 90 , 120 , 150 in that order. Find its area. Proposed by: Yuan Yao p 3+ 3 Answer: 2 ⇣ ⌘ p 3 3 The area of this hexagon is the area of a ⇥ 1 + rectangle (with the 90 angles of the hexagon 2 2 at opposite vertices) minus the area of an equilateral triangle with side length 1. Then this is p p p 6 + 3 3 3 3 + 3 = . 4 4 2