Step-by-step explanation:
just in case a few words about area and the difference to distance :
to measure distance we define a basic unit of length (like 1 inch or 1 ft or 1 meter or ...), and then we analyze for a given distance how often that basic unit fits inside that distance.
we do the save thing with "area". just instead of a basic unit of length we create a basic unit of area and then check how often it fits into the given area.
such a basic unit of area is typically defined by 2 dimensions of length and width, and in most cases we select a square (length = width) like 1 in², 1 ft², 1 yd², 1 cm², 1 m², ...
for area like a square or a rectangle you can imagine the following :
we lay first one row of basic area units at the edge of the measured area. and then we continue to lay one more row, and one more row, and one more ... until we reach the opposite end.
by counting the "used" basic areas we know the total area.
how do we do that ?
well, we know how many are in the first row. that is what e.g. the length of the area tells us.
and then we did the exact same thing several TIMES to fill the following rows. you see that ? TIMES !
so, if the area is n basic units long, and we can fit m rows in (because it is m units wide, or the width is m units long), then the area is n×m area units.
that is how the area of squares and rectangles work.
the only "specialty" of squares is that the length = the width.
but the principle is still the same :
the area of a rectangle is the mentioned product n×m. and if n=m, then we have n×n = n².
and that is the reason for the name "square" of a square, or when we multiply a number by itself for any other reason.
the formula always matters, because it contains the structure of the object or system we want to do some calculation about. the formula has to fit precisely to the calculated object, or we calculate apples for a system of oranges. we can do that, but normally it does not make any sense.
