1 inch = 0.0254 meters
1 inch * 1 inch = 0.0254 meters * 0.0254 meters
1 inch squared = 0.00064516 meters squared
I think maybe you have been misinformed.
The yard is defined in terms of the metre. (source) I learned it as the inch being defined in terms of centimetre which amounts to the same thing.
The metre is defined in terms of the speed of light traveling at a certain fraction of a second. (source)
The second is defined in terms of the radioactivity of the caesium 133 atom. (source)
By the way I wasn't contradicting Educated's post; I realise they are the same precision/accuracy. I mentioned that I like to use 1 inch = 2.54 cm as a general statement; for example, I would generally not use 1 mile 1.61 km but instead convert the long way.