2001 AMC 10 Problem 18

Question

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:area ratio tiling percentage

Difficulty rating: 1530

Small hint:

Work within a repeating

3\times3

block of small squares

Big hint:

Of the

9

small squares,

4

lie outside the pentagons

Solution:

Consider a repeating

3\times3

block of nine small squares. Four of these nine squares are not part of the pentagons, so the pentagons cover

1-\dfrac49=\dfrac59\approx55.6\%

of the area.

This is closest to

56.

Thus, the correct answer is D.