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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?