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CEMC Cayley

Geometry Difficulty 2.0 Junior Find the answer

What is the perimeter of the shaded region in a 3×3 3 \times 3 grid where some 1×1 1 \times 1 squares are shaded?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

The top, left and bottom unit squares each contribute 3 sides of length 1 to the perimeter. The remaining square contributes 1 side of length 1 to the perimeter. Therefore, the perimeter is 3×3+1×1=10 3 \times 3 + 1 \times 1 = 10 .

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