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MathNet 2026 — Part 02 Question 25

Math Olympiad Vault · MathNet 2026 — Part 02

Question 25

Diogo cut out a cardboard cross as shown below. On this cross, all sides have a length equal to $1~\mathrm{cm}$, and all angles are right. Fernanda challenged Diogo to make two straight cuts on this cross, in order to form four pieces that can be re-embedded in order to form a square. Question illustration
a) What will be the area of the obtained square?
b) What will be the side of the obtained square?
c) Show how Diogo can make these two straight cuts so that he can form the square with the four pieces obtained by the cut!