AMC 8 1990 Problem 3
AMC8 1990 年第 3 题
面积与周长（综合）★★☆☆☆
What fraction of the square is shaded?
着色部分占正方形的几分之几？
- A.
- B.
- C.
- D.
- E.
正确答案 · Correct Answer
E
解析 · Solution
Solution 1
Swap the two trapezoids in the middle layer, as shown. The shaded region and unshaded region now form congruent triangles, of the square is shaded.
Notice that the figure is made of 3 pairs of congruent shapes, and each of these pairs has 1 shaded and 1 unshaded shape. Therefore, of the square is shaded.
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