Need help with a quant question

[DeleteMePlease]

When practising with powerprep I ran into a question that said a square is inscribed in another square. And then they wanted to know the size of the inner square.

 

And to be honest I don't really understand what they mean. How can a square be inscribed in another one, without them having the same size? Sadly, powerprep doesn't supply you with an explanation, so I don't know how to understand this question.

[Yetanotherdegree]

Picture a square with a diamond inside it, where the diamond is obviously smaller because it is fully contained within the original square and there is leftover space at each of the main square's corners. It sounds like this might be what is being described, and in this case the area of the inside square is half of that of the main square (you can visualize this by drawing lines connecting the corners of the diamond, in which case you get 8 equal triangles, four of which are inside the diamond)

What was the actual question?