I didn't miscalculate, you are citing a completely different measure. I cited the linear diagonal screen size that is used as the descriptive size. Area is a completely different measure and can be misleading.
For practical purposes what is the improvement in viewable height or width of content? For width it's less than 8%, for height it's 8%, neither is a notable difference, and shows that the diagonal size difference of less than 7% is a good proxy, certainly better than area.
Oh, I already intended to, and you should take up my suggestion to try holding one for five minutes while watching a video the next time you are at an Apple store.
-R