2023 AMC 8 第 19 题
先试着解答 2023 AMC 8 第 19 题，然后核对你的答案与视频与精心整理的解答，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 2023 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。
19.
一个等边三角形放在一个更大的等边三角形内部，使得它们之间的区域可分成三个全等的梯形，如下图所示。内三角形边长是大三角形边长的 。一个梯形的面积与内三角形的面积之比是多少？
An equilateral triangle is placed inside a larger equilateral triangle so that the region between them can be divided into three congruent trapezoids, as shown below. The side length of the inner triangle is the side length of the larger triangle. What is the ratio of the area of one trapezoid to the area of the inner triangle?
小提示：
相似三角形面积按边长比例的平方缩放
Areas of similar triangles scale as the square of side lengths
大提示：
内三角形面积是大三角形面积的
The inner triangle has of the large triangle’s area
视频讲解：
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文字解答：
内三角形边长是大三角形的 ，所以面积是大三角形的 。
三个梯形总面积是大三角形的 。
一个梯形面积是大三角形的 。
它与内三角形的面积比为
所以正确答案是 C。
Since the inner triangle’s side length is the side length of the outer triangle, its area is the area of the outer triangle.
This means that the three trapezoids are the area of the outer triangle.
Therefore, one trapezoid is the area of the outer triangle.
This makes the ratio of the areas of one trapezoid and the inner triangle
Thus, C is the correct answer.
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