A4 A square cage measuring $90 \times 90 \, \text{cm}$ has in the middle of each wall a door that is $70 \, \text{cm}$ wide. The four doors are swung inward, starting at the same moment and at the same speed. At a certain moment, they can no longer rotate and then enclose a square (see the figure with two top views of intermediate positions).
![](https://cdn.mathpix.com/cropped/2024_04_17_3de5ef26943dd9bef1e9g-2.jpg?height=358&width=742&top_left_y=175&top_left_x=1178)

Calculate the area of the enclosed square.
A4. See figure: $AB=80, AC=10$

so $BC^2=80^2+10^2=6500$.

$CD^2+BD^2=6500$, so $CD^2=6500-70^2=1600$.

Thus $CD=40$ and $DE=CE-CD=70-40=30$.

Therefore, the required area is 900.

![](https://cdn.mathpix.com/cropped/2024_04_17_4ac1047f88758396ef6dg-1.jpg?height=454&width=462&top_left_y=1115&top_left_x=1211)