1986 AMC 8 第 13 题

先试着解答 1986 AMC 8 第 13 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1986 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

13.

图中多边形的周长是
The perimeter of the polygon shown is
1414
2020
2828
4848
无法由给定信息确定
cannot be determined from the information given
答案:C
知识点:周长矩形
小提示:
所有角都是直角,所以水平边和竖直边都可以分别重新组合
All the angles are right angles, so the horizontal edges and the vertical edges can each be regrouped
大提示:
向右和向左的水平边都各自跨过总宽 88,向上和向下的竖直边也都各自跨过总高 66
The rightward and leftward horizontal edges each span the full width 8,8, and the upward and downward vertical edges each span the full height 66
解答:
因为每个角都是直角,把边平移重组可见,水平边总共走过宽度两次,竖直边走过高度两次。因此周长等于完整 88 乘 66 矩形的周长,即 2(8+6)=282(8 + 6) = 28。
答案不取决于缺口具体切在哪里。
所以正确答案是 C。
Because every angle is a right angle, sliding the edges shows that the horizontal edges together traverse the width twice and the vertical edges traverse the height twice. So the perimeter equals that of the full 88 by 66 rectangle, 2(8+6)=28.2(8 + 6) = 28.
The answer does not depend on exactly where the notch is cut.
Thus, the correct answer is C .
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