Why is the unit of image size not Pixel²?

If you calculate the area of a rectangle, you just multiply the height and the width and get back the unit squared. Example: 5cm * 10cm = 50cm² In contrast, if you calculate the size of an image, you also multiply the height and the width, but you get back the unit - Pixel - just as it was the unit of the height and width before multiplying. Example: What you actually calculate is the following: 3840 Pixel * 2160 Pixel = 8294400 Pixel What I would expect is: 3840 Pixel * 2160 Pixel = 8294400 Pixel² Why is that the unit at multiplying Pixels is not being squared?