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Geometry Difficulty 1.1 Junior Find the answer Canada

Some of the $1 \times 1$ squares in a $3 \times 3$ grid are shaded, as shown.

What is the perimeter of the shaded region?

Pick one

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 $3 \times 3 + 1 \times 1 = 10$ .

Alternatively, the perimeter includes 3 vertical right sides, 3 vertical left sides, 2 horizontal top sides, and 2 horizontal bottom sides, which means that the perimeter is $3+3+2+2=10$ .

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.