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- TL;DR Summary
- Relationship of inclined area with respect to original area

Hi, I have a problem with inclined planes. The idea is to calculate the stress in an inclined plane of a bar under tension for which you need the surface. I have no idea how this surface is derived, though. In the attached file, you can see what I mean. For a rectangular cross-section, it's straightforward, just applying the rectangle area with the new inclined length. Now, everywhere I see, everyone uses the same rectangular bar as an example.

However, in one single textbook, the exercise uses an elliptical cross-section to seemingly represent a random surface. They use the same formula for the area, but without any explanation, apparently trivially and immediately deriving, but I don't see why the area of an inclined elliptical surface with respect to the original surface is the same as the rectangular one.

My suspicion is that it has to do with the vector area which, being the same direction as the normal, is somehow projected onto the other's area vector, but I don't see it. Thanks for the help.

However, in one single textbook, the exercise uses an elliptical cross-section to seemingly represent a random surface. They use the same formula for the area, but without any explanation, apparently trivially and immediately deriving, but I don't see why the area of an inclined elliptical surface with respect to the original surface is the same as the rectangular one.

My suspicion is that it has to do with the vector area which, being the same direction as the normal, is somehow projected onto the other's area vector, but I don't see it. Thanks for the help.