Problem 11 · 2015 Math Kangaroo
Stretch
Geometry & Measurement
perimetergrid-counting
Thomas has made the following shape with 6 squares of side length 1. What is the perimeter of the shape?
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Answer: D — 12
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Hint 1 of 2
Six separate squares have 24 unit edges in total; gluing them hides edges in pairs.
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Hint 2 of 2
Every place two squares touch removes 2 from the perimeter, so count the touching pairs.
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Approach: start from 6 separate squares and subtract the hidden edges
- Six unit squares apart have 6 × 4 = 24 edges of length 1.
- In this stacked shape the squares touch along 6 internal edges; each shared edge hides 2 unit lengths from the outline.
- So the perimeter is 24 − 2 × 6 = 12.
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