AMC 8 1994 Problem 12
AMC8 1994 年第 12 题
面积与周长（综合）★★★☆☆
Each of the three large squares shown below is the same size. Segments that intersect the sides of the squares intersect at the midpoints of the sides. How do the shaded areas of these squares compare?
下面所示的三个大正方形大小相同。与正方形边相交的线段在边的中点处相交。这些正方形的着色面积相比如何？
- A.The shaded areas in all three are equal. / 三个图形的阴影面积都相等。
- B.Only the shaded areas of I and II are equal. / 只有 I 和 II 的阴影面积相等。
- C.Only the shaded areas of I and III are equal. / 只有 I 和 III 的阴影面积相等。
- D.Only the shaded areas of II and III are equal. / 只有 II 和 III 的阴影面积相等。
- E.The shaded areas of I, II and III are all different. / I、II 和 III 的阴影面积各不相同。
正确答案 · Correct Answer
A
解析 · Solution
Solution 1
Square II clearly has 1/4 shaded. Partitioning square I into eight right triangles also shows 1/4 of it is shaded. Lastly, square III can be partitioned into sixteen triangles, and because four are shaded, 1/4 of the total square is shaded. .
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