AMC10 2001 A

AMC10 2001 A · Q18

AMC10 2001 A · Q18. It mainly tests Percent, Area & perimeter.

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

平面被全等的正方形和全等的五边形如图所示铺满。五边形包围的平面百分比最接近

(A) 50 50

(B) 52 52

(D) 56 56

(E) 58 58

Answer

Correct choice: (D)

正确答案：（D）

Solution

(D) The pattern shown at left is repeated in the plane. In fact, nine repetitions of it are shown in the statement of the problem. Note that four of the nine squares in the three-by-three square are not in the four pentagons that make up the three-by-three square. Therefore, the percentage of the plane that is enclosed by pentagons is $1-\dfrac{4}{9}=\dfrac{5}{9}=55\dfrac{5}{9}\%$

（D）左边所示的图案在平面上重复出现。事实上，题目陈述中展示了它的九次重复。注意，在这个 $3\times 3$ 的正方形中，九个小正方形里有四个不在构成该 $3\times 3$ 正方形的四个五边形内。因此，被五边形围成的平面所占百分比为 $1-\dfrac{4}{9}=\dfrac{5}{9}=55\dfrac{5}{9}\%$

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