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# Measuring rectangles with different unit squares

Video transcript

I have two identical
rectangles here, and I want to measure how
much space each of them take up on the
plane of my screen, the screen that you are
looking at right now. And I want to do it using
two different units. It's clear, since they're
two identical rectangles, that they take up the
exact same amount of space. They will have the same area. But what we could see
it that we can measure that area using different units. So first over here, let's
say that this figure is 1 foot in width. And it is also 1 foot in height. So this right over here
is equal to 1 square foot. It's clearly a square. It has the same width
and the same height. And each of these
dimensions are 1 foot, so we could call
it 1 square foot. So let's see how
many square feet we can get onto one
of these rectangles, and essentially we'll
be measuring its area in terms of square feet. And so we want to
cover the entire space without overlapping and without
going over the boundary. So that's 1, 2, 3, 4, 5, and 6. 6 in that first row, and then
I have 7, 8, 9 10, 11, and 12. So that looks like this area,
which is the same as this area down here. If I were to measure
it in square feet, the area is equal to,
let me write this down, the area is equal to, we
have-- let me write it down. We have 1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, 12 square feet. 12 square feet. Now, I'm going to try to
measure that same area in a different
unit, and I'm going to just make up this unit. I'm going to call it a furgle. And a furgle in one dimension,
so a furgle in one dimension is twice a foot. So that distance
right over here, I'm going to call a furgle. That's one furgle. This is something
that I made up just for the purpose of this video. Most people will not
recognize what a furgle is. So its height is one furgle. Its width is a furgle. And so we could say that
this is 1 square furgle. So let's see how many
square furgles is this area, that same area
that is 12 square feet. So let me copy and paste this. So let me copy, and then paste. So let's see if we can get
one square furgle on there. We can get another
square furgle on there, and we can get a third
square furgle on there. So we get 1, 2,
3 square furgles. The area of this figure in
furgles, square furgles, I should say, area is
equal to 3 square furgles. So it's the same exact area. 3 square furgles is equal
to 12 square feet, covering the exact same area. Now, what I encourage
you to think about is how many square feet
make a square furgle?