Problem 14 · 2025 Math Kangaroo
Hard
Geometry & Measurement
areaperimeter
Jana cuts four small squares of the same size from the corners of a square piece of paper (see picture). The total cut-away area is 16 cm², and the area of the remaining figure (the cross) is 9 cm². What is the perimeter of the cross?
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Answer: C — 20 cm
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Hint 1 of 2
The whole square’s area is the cut-away plus the cross.
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Hint 2 of 2
Cutting a square out of a corner doesn’t change the perimeter — the removed edges are replaced by equal new edges.
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Approach: reassemble area, then track perimeter
- Original square area = 16 (cut away) + 9 (cross) = 25, so its side is 5.
- Each of the four corner squares has area 16 ÷ 4 = 4, so side 2.
- Removing a 2×2 square from a corner replaces two outer edges with two equal inner edges, so the perimeter stays the same.
- The cross perimeter equals the square’s perimeter: 4 × 5 = 20 cm.
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