【Haichuan Teahouse】Brain-teasing Series: Answers Derived from Central Deductive Analysis
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Title: As shown in the figure, two identical squares are placed such that a vertex of one square is at the center of the other square. Find the area of the shaded region. This is a question from the entrance examination for middle school in a key high school in Tianjin. It really confuses many elementary school students, who think there isn’t enough information; however, through careful reasoning and analysis, a solution can be found. Have you thought of a way?
This post was last edited by Wang Genrong on 2021-7-9 09:40; the value is 24.
Since 4 is in the middle no matter how it’s rotated, it’s equivalent to 24;P
The area of the two squares is 16+16=32
Let’s consider an extreme case: it rotates exactly into a triangular shape
Another extreme is a small square in the middle……
The shaded area on the left = 16-4=12. The same on the right. It’s not a shadow being overlaid, is it? (At least it isn’t indicated in the diagram), so I think it’s 24.
Is this 24 a constant value, or is it the maximum or minimum value?