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Transitioning from unit squares to area formula

Lindsay finds the area of a rectangle both by counting unit squares and multiplying side lengths.  Created by Lindsay Spears.

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Video transcript

- [Voiceover] This square is 1 square unit, so what is the area of Rectangle A? The first thing we're told is that each of these little squares equal 1 square unit, and then, we're asked to find the area of Rectangle A. Here's Rectangle A, and area is the space that it covers. So how much space does Rectangle A cover? How many square units does Rectangle A cover? One way to answer that would be count how many square units it covers, except they've covered up our square units. So, one idea's we could draw them back. Say you cover'em up, we'll draw them back in. So goin' like this, connect all these, and then, we should be able to count our square units. So we have one, two, three, four, five six, seven, eight, nine, 10, 11, 12. 12 square units. Rectangle A covers 12 square units, so it has an area of 12 square units. But this isn't the only way that we could've solved this. We could've also said, we could've also looked at this and said, okay, this top row is four square units long. One, two, three, four, has a length of four units. So that means the top row will have one, two, three, four square units inside of it. And then we coulda looked over on the side, over here, and said, well, how many rows of four will they'll be? It'll be one, two, three rows of four. So we'll have this row of four, and then a second row of four, and a third. So three times, we will have four square units. There's four square units at the top, another in the middle, and another at the bottom. Three times, we will have four square units. Or, we could go even farther than that. So we coulda done three times four, or we could look at this and say, okay, here's one column. This column has three square units. It has a length of three. One, two, three. How many of these columns like this will there be? There'll be one, two, three, four, 'cause our length here at the top is four. So, this time, four times, we will see three square units. One, two, three, and we'll see that one, two, three, four times. So, no matter which of these we solved, whether we counted the square units like in the beginning, or we multiplied the side lengths, the three and the four, in every case, we're gonna find that this equals 12 square units. The area of Rectangle A is 12 square units because it covers 12 square units.