# How can I calculate this difference in length when a rectangle is rotated by 10 degrees?

I have a rectangle x=1000 y=400. I have a 2nd rectangle with the same size on top of it. I rotate the second rectangle 10 degrees around one of the points. If I place measuring lines perpendicular to the 1st (not rotated) rectangle, but use the outer most edges, I will see that the 2nd (rotated) rectangle is now longer because of the displacement. Please refer to the attached image.

How can I calculate this difference in length with any given contour lengths?

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