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AMC 12 2001 Problem 10

  • Paper

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

(A) 50(B) 52(C) 54(D) 56(E) 58\text{(A) }50 \text{(B) }52 \text{(C) }54 \text{(D) }56 \text{(E) }58

unitsize(3mm);
defaultpen(linewidth(0.8pt));

path p1=(0,0)--(3,0)--(3,3)--(0,3)--(0,0);
path p2=(0,1)--(1,1)--(1,0);
path p3=(2,0)--(2,1)--(3,1);
path p4=(3,2)--(2,2)--(2,3);
path p5=(1,3)--(1,2)--(0,2);
path p6=(1,1)--(2,2);
path p7=(2,1)--(1,2);
path[] p=p1^^p2^^p3^^p4^^p5^^p6^^p7;
for(int i=0; i<3; ++i)
{
for(int j=0; j<3; ++j)
{
draw(shift(3*i,3*j)*p);
}
}

Dataset text AMC 12 2000 to 2025. Quoted with source.

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D

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