How to convert camera sensor size designation to sensor surface in mm2?

[dex90]

I can’t seem to spot the correlation between numbers like:
1" (13.2 x 8.8 mm)
1/1.7" (~ 7.53 x 5.64 mm)

Taken from: Digital Camera Sensor Sizes

Or:
1" (12.8 x 9.6 mm)
1/1.7" (~ 7.6 x 5.70 mm)

Taken from image on Camera Sensor Sizes (and Why They Matter)
How come these 2 sites state different width and height for same sensor designations and what is the actual way to calculate the WxH? Is there even one or is this nomenclature just an agreement?

Edit: I found a method to get a diagonal length in mm from the sensor designation in inches. The solution, as bizarre as it is to me, is to multiply the sensor designation in inches with the number 16 and that gives us the length of the diagonal in milimiteres Hilarious. And then I can get the screen/image ratio form the resolution and I can get W and H in millimeters.

I still don't know why the 2 sites I linked above got different W and H numbers for same sensors. Oh, could it be due to different aspect ratio? I spent over an hour researching this, manufacturers should just add in their camera specs the physical pixel size and it would be fine.