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# Counting unit squares to find area formula

CCSS.Math:

## Video transcript

I've got three rectangles here and I also have their their dimensions I have their height and their width in fact this one right here has the same height and width so this is actually a square so let's think about how much space they each take up on my screen and since we're doing everything in terms of meters since all of the dimensions are in meters I'm going to measure the area in terms of square meters so let's see how many square meters I can fit onto this yellow rectangle without going outside of its boundary and without overlapping so I can fit one square meter remember a square meter is just a square where its length is one meter and its width is one meter so that's one square meter two three four or five five and six square meters so we see here that the area that the area is 6 square meters area is equal to 6 square square meters but something might be jumping out at you did I really have to sit and count 1 2 3 4 5 6 you might have recognized that I could view this as really two groups of three let me make that very clear so for example I could view this as one group of three one group of three and then another group of three now how did I get groups of three well that's because the width here is three meters so I could put three I could put three square meters side-by-side and how did I get the two groups well it's two meters this has the length of two meters so another way that I could have essentially counted these six things is I could have said look I have a length of two meters so I'm going to have two groups of three I'm going to have two groups of three so I could multiply two times three two times three two times two of my groups of three and I would have gotten six and I would have gotten six so I could and you might say hey wait is this just a coincidence that if I took the the height or if I took the length and I multiplied it by the width that I get the same thing as its area and no it's not because when you took the the length you essentially said well how many rows do I have and then you say when you multiply it by the width you're saying well how many squares do I or how many of these how many of these square meters can I fit into a row so this is a really a quick way of counting how many of these square meters you have so you could say that two meters multiplied by three meters multiplied by three meters is equal to 6 square meters is equal to 6 square square meters now you might say hey I'm not sure if that always applies let's see if it applies to these other rectangles right over here so based on what we just saw let's take the length 4 meters let's take the length 4 meters and multiplied by the width and multiplied by 2 meters 2 meters now 4 times 2 is 8 so this should give us 8 square 8 square meters let's see if this is actually the case so 1 2 3 4 5 and you see it's going in the right direction 5 6 7 7 & 8 so the area of this rectangle is indeed 8 square meters and you could view this as 4 groups of 2 so you could literally view this as 4 groups of 2 that's where the 4 times 2 comes from so you could view it as 4 groups of 2 like this or you could view it as 2 groups of 4 so one group of 4 right over here so you could view this as 2 times 4 and then two groups two groups of 4 I want to draw it a little bit cleaner now you could probably figure out what the area of this rectangle is actually a square has the same length and the same width we multiply the length 3 meters times the width so times three meters to get three times three is nine nine square nine square meters nine square meters and let's verify it again just to feel really good about this multiplying the dimensions of these rectangles so we have one two three four five six seven eight and nine so it matches up we figure out how many square meters can we can we cover this thing with without overlapping without going into the boundaries we get the exact same thing as if we multiplied three times three if we multiply the length times the width in meters