2001 AMC 12 第 10 题

Question

平面按图所示由全等的正方形和全等的五边形铺成。被五边形覆盖的平面面积百分比最接近

The plane is tiled by congruent squares and congruent pentagons as indicated. The percent of the plane that is enclosed by the pentagons is closest to

50

52

54

56

58

答案：D

知识点：铺砖面积百分数

难度评级：1480

小提示：

图案以

3 \times 3

个单位正方形为一组重复

The pattern repeats in blocks of

3 \times 3

unit squares

大提示：

每一组中，保持为正方形的四个小方格占总面积的

\dfrac{4}{9}

In each block, the four squares that stay square make up

\dfrac{4}{9}

of the area

解答：

图案在一个由九个单位正方形组成的

3 \times 3

方块中重复。其中九个小方格有四个未被五边形覆盖；剩余面积属于五边形。

所以五边形覆盖的比例为

1 - \dfrac{4}{9} = \dfrac{5}{9} = 55.5\overline{5}\%\text{，}

最接近

56

。

因此，正确答案是 D。

The pattern repeats over a

3 \times 3

block of nine unit squares. Four of these nine squares are not covered by pentagons; the rest of the area belongs to the pentagons.

So the pentagons enclose

1 - \dfrac{4}{9} = \dfrac{5}{9} = 55.5\overline{5}\%,

which is closest to

56.

Thus, the correct answer is D.

2001 AMC 12 第 10 题

答案：D

难度评级：1480

小提示：

大提示：

解答：

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