3420.22 – The Area of a Cross

The cross below is composed of five congruent squares. What is its area?

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Solution

In triangle ABC, we have

w2+(2w)2=102⇝5w2=100⇝w2=20. w^2 + (2w)^2 = 10^2 \leadsto 5w^2 = 100 \leadsto w^2 = 20.

Thus each small square has area 2020, and the total area is 100100.

That's it for the problem, but since 100=102100 = 10^2 don't you wonder whether the cross can be cut into pieces and re-arranged as a 10×1010 \times 10 square?

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