Question

Peter lives near a rectangular field that is filled with blackberry bushes. The field is $10$ meters long and $8$ meters wide, and Peter can reach any blackberries that are within $1$ meter of an edge of the field. The portion of the field he can reach is shaded in the figure below. What fraction of the area of the field can Peter reach?

$\dfrac{1}{6}$

$\dfrac{1}{4}$

$\dfrac{1}{3}$

$\dfrac{3}{8}$

$\dfrac{2}{5}$

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Written solution:

The whole field has area $10\cdot8=80$ . The unreachable inner rectangle is $8$ meters by $6$ meters, with area $48$ . Thus the reachable area is $80-48=32$ , and the fraction is $32/80=2/5$ .

2026 AMC 8 Problem 6

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Problem 6 in Other Years