Measuring area with tiled square units

What we're going to do in this video is look at two rectangles that have the exact same area, and we're going to measure each of them with a different square unit.

So, this top unit right over here, this is a square foot. That means its height is one foot and its width right here is one foot. Now, this square unit over here, this is completely made up, and I am going to call this a voot or vout. So, this right over here is one foot, and this over here, the width is one foot.

So, this entire thing is one square foot, while this top one, of course, is one square foot. Now, let's measure each of the... let's measure the top rectangle in terms of square feet, and let's measure the bottom rectangle in terms of square, I guess I could say, vt.

All right, so first, the top rectangle. So we have one, two square feet, three square feet, four square feet, five square feet, and then we have, looks like, six square feet. And then we're gonna need to have another six square feet down here, so that's seven, eight, nine, ten, eleven, and twelve.

So, when I tile the square feet onto our original rectangle, looks like we have twelve square feet. And so I could write its area like this: twelve square feet.

Now, what about this one in terms of feet? And one, you could have a square foot or many square feet. Let me do the same exercise here: that's one square foot, this is two square feet, I could say, and then this is three square feet.

So, the same area could either be twelve square feet, or it could be three square square feet. And I want you to think about whether that makes sense. Think about how many square feet would make up one square foot.

In fact, we can figure that out on our own right over here. So, that's one square foot, this is two square feet, this is three square feet, and then four square feet.

So, it looks like four square feet make up one square foot. And so think about, does it make sense that three square feet is the same thing as twelve square feet?