Work through 2026 AMC 8 Problem 6 on area and fractions with a written solution, hints, and a visual explanation.
GeometryLevel 2 · Core skill
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?
Diagram 1
A. 1/6
B. 1/4
C. 1/3
D. 3/8
E. 2/5
Hints
It's easier to find the region Peter can't reach than the region he can.
The unreachable region is a smaller rectangle, shrunk by 1 meter on every side.
Subtract the inner rectangle's area from the total area, then write that reachable area as a fraction of the whole field.
Read the step-by-step solution
Answer: E · 2/5
Find reachable area
Total area = 10 × 8 = 80. The unreachable interior is (10 − 2) × (8 − 2) = 8 × 6 = 48.
