In the past two months, I had found a wonderful pdf that went through a derivation of the determinant with calculating the area of a parallelepiped as its starting point. The document did not get into the weeds of calculating the determinant given a matrix or even focus explicitly on matrices at all; it was probably the single best description of why the determinant tells us about area I had found and I just really found the document's approach to determinants extremely useful.
I'm trying to relocate this pdf to no avail and was really helping someone could help me find it.
What I remember is this: it begins with calculating the area of a parallelogram as its starting point. It describes how we want the area to change when a side is scaled and when the image is sheared (I very distinctly remembering these two things being bulleted in the first page of the paper) and goes onto describe how these properties would manifest in a general "area function," that is a function that takes in the vectors as inputs and returns some type of unsigned area. It proves several facts about these functions that begin to show how the determinant "appears" from answering this question naturally.
After this point, they expand their scope to signed area functions and, building upon the results in the first part, show that any function which returns the signed area of a parallelogram is simply a multiple of the determinant.
The paper rounds out with a discussion about expanding these ideas to higher dimensions; it describes the problem of measuring the area of a higher dimensional parallelepiped with regards to measuring the area of its shadow. One of the more distinct parts of this description is that it begins with a hypothetical scenario where you find a floating parallelepiped outside of your window one day and cannot interact with it but wish to find its area.
My attempts at googling with these bits of information I remember have not been fruitful, so any help finding this pdf would be appreciated.