eli5 How do decimals and units of area measurement work?

Question

0.9cmx0.9cm = 0.81cm²
9mmx9mm = 81mm²
Do these two numbers equate?

In: 0

Answer 1

It makes sense when you understand that the a “centimeter” and a “square centimeter” measure different things: the former, distance; the latter, *area*.

You cannot measure distance in square centimeters, nor area in centimeters.

So if you have a square that is 0.5 cm by 0.5 cm, it has an area that is 0.25 cm^2 which seems weird until you put 4 of these squares together to form a bigger square of 1 cm by 1 cm, the area of which is . . . 1 cm^2 .