So we've got two figures right over here,
and I want to think about how much space they take up
on your screen.
And this idea of how much space something takes up
on a surface, this idea is area.
So right when you look at it, it looks pretty clear
that this purple figure takes up more space
on my screen than this blue figure.
But how do we actually measure it?
How do we actually know how much more area this purple figure
takes up than this blue one?
Well, one way to do it would be to define
a unit amount of area.
So, for example, I could create a square right over here,
and this square, whatever units we're using, we could say it's
a one unit.
So if its width right over here is one unit
and its height right over here is one unit,
we could call this a unit square.
And so one way to measure the area of these figures
is to figure out how many unit squares I could cover
this thing with without overlapping
and while staying in the boundaries.
So let's try to do that.
Let's try to cover each of these with unit squares,
and essentially we'll have a measure of area.
So I'll start with this blue one.
So we could put 1, 2, 3, 3, 4, 5, five unit squares.
Let me write this down.
So we got 1, 2, 3, 4, 5 unit squares,
and I could draw the boundary between those unit
squares a little bit clearer.
So we have 5 unit squares.
And so we could say that this figure right over here
has an area.
The area is 5.
We could say 5 unit squares.
The more typical way of saying it
is that you have 5 square units.
That's the area over here.
Now, let's do the same thing with this purple figure.
So with the purple figure, I could put 1, 2, 3, 4, 5, 6, 7,
8, 9, 10 of these unit squares.
I can cover it.
They're not overlapping, or I'm trying pretty close
to not make them overlap.
You see, you can fit 10 of them.
And let me draw the boundary between them,
so you can see a little bit clearer.
So that's the boundary between my unit squares.
So I think-- there you go.
And we can count them.
We have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
So we could say the area here-- and let me actually
divide these with the black boundary, too.
It makes it a little bit clearer than that blue.
So the area here for the purple figure, we could say,
so the area here is equal to 10.
10 square, 10 square units.
So what we have here, we have an idea
of how much space does something take up on a surface.
And you could eyeball it, and say, hey, this
takes up more space.
But now we've come up with a way of measuring it.
We can define a unit square.
Here it's a 1 unit by 1 unit.
In the future we'll see that it could be a unit centimeter.
It could be a 1 centimeter by 1 centimeter squared.
It could be a 1 meter by 1 meter squared.
It could be a 1 foot by 1 foot square,
but then we can use that to actually measure
the area of things.
This thing has an area of 5 square units.
This thing has an area of 10 square units.
So this one we can actually say has twice the area.
The purple figure had twice the area--
it's 10 square units-- as the blue figure.
It takes up twice the amount of space on the screen.