2001 AMC 12 Problem 10

Attempt Problem 10 of the 2001 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2001 AMC 12 solutions, or check the answer key.

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10.

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

Answer: D

Concepts:tiling area percentage

Difficulty rating: 1480

Small hint:

The pattern repeats in blocks of

3 \times 3

unit squares

Big hint:

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

\dfrac{4}{9}

of the area

Solution:

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.