HMMT 十一月 2014 · 冲刺赛 · 第 6 题

HMMT November 2014 — Guts Round — Problem 6

[ 6 ] In the octagon COM P U T ER exhibited below, all interior angles are either 90 or 270 and we have CO = OM = M P = P U = U T = T E = 1. T E P U D O M C R Point D (not to scale in the diagram) is selected on segment RE so that polygons COM P U T ED and CDR have the same area. Find DR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HMMT NOVEMBER 2014, 15 NOVEMBER 2014 — GUTS ROUND Organization Team Team ID#

解析

[ 6 ] In the octagon COM P U T ER exhibited below, all interior angles are either 90 or 270 and we have CO = OM = M P = P U = U T = T E = 1. T E P U D O M C R Point D (not to scale in the diagram) is selected on segment RE so that polygons COM P U T ED and CDR have the same area. Find DR . Answer: 2 The area of the octagon COM P U T ER is equal to 6. So, the area of CDR must be 1