1998 AMC 8 第 6 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

6.

点在水平方向和竖直方向上都相隔一个单位。这个多边形围成的面积是多少平方单位?

Dots are spaced one unit apart, horizontally and vertically. The number of square units enclosed by the polygon is

55

66

77

88

99

答案:B
知识点:面积分割格点
难度评级:870
解答:

观察底部的 2×32 \times 3 长方形。图形从这个 2×32 \times 3 长方形底部去掉一块面积,又在顶部加上同样面积,因此面积为 66

所以正确答案是 B

Consider the 2×32 \times 3 rectangle on the bottom. The triangular piece above that rectangle has the same area as the missing triangular piece below it. Rearranging one into the other gives a full 2×32 \times 3 rectangle, so the polygon's area is 66.

Thus, the correct answer is B .

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