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HMMT 十一月 2014 · GEN 赛 · 第 4 题

HMMT November 2014 — GEN Round — Problem 4

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. In rectangle ABCD with area 1, point M is selected on AB and points X , Y are selected on CD suchthat AX < AY . Suppose that AM = BM . Given that the area of triangle M XY is , compute 1
    2014
    the area of trapezoid AXY B .
解析

英文解析

  1. In rectangle ABCD with area 1, point M is selected on AB and points X , Y are selected on CD suchthat AX < AY . Suppose that AM = BM . Given that the area of triangle M XY is , compute 1
    2014
    the area of trapezoid AXY B .
    1 1 504 1 1
    Answer: + OR Notice that [ AM X ] + [ BY M ] = [ ABCD ] = . Thus,
    2 2014 1007 2 2
    1 1 504
    [ AXY B ] = [ AM X ] + [ BY M ] + [ M XY ] = + =
    2 2014 1007