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Decomposing shapes to find area: add

Let's find the area of an irregular 10-sided shape by breaking it into smaller rectangles. We'll learn to decompose complex shapes, calculate the area of each rectangle, and combine those areas to find the total area, making the topic engaging and enjoyable. Created by Lindsay Spears.

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Video transcript

- [Voiceover] What is the area of the figure? So down here we have this one, two, three, four, five, six, seven, eight, nine, 10-sided figure, and we want to know its area, how many square meters does this figure cover? And we have some measurements, that seems helpful, but what's not too helpful to me is I don't know the special trick to find the area of a 10-sided figure so I've got to think about what I do know and what I do know is the way to find area of a rectangle. So what I can do, because I can see, if I can find any rectangles in here. Here's one rectangle, right there. So I can find the area of that part. Then let's see if I can find any more. Here's another rectangle. So I can find the area of that part. We could call that one a rectangle or a square. And then that leaves us with this last part, which is again, a rectangle. So what we did is, we broke this up or decomposed it into three rectangles and now if I find out how much space this purple one covers, and the blue one and the green one, if I combine those, that would tell me the area of the entire figure, how much space the entire figure covers. So let's start with this one right here. This one is three meters long, so we can kind of divide that by three meters, into three equal meters, and then we've got a width of two meters down here so we can split that in half. So if we draw those lines out, we can see this top row is going to cover one square meter, two square meters, three square meters, and then there's two rows of that, so there's two rows of three square meters for a total of six square meters. This rectangle covers six square meters, so this part of the entire figure covers six square meters. The next one, our measurements are three and a three, so it will have three rows of three square meters or nine square meters, and then finally this purple one has three meters and nine, so we can say it will have three rows of nine or nine rows of three square meters which is 27 square meters. So the area of this purple section, it covers completely 27 square meters. The green covers nine square meters, and the blue covered six square meters. So, if we combine all those areas, all those square meters it covers, that will tell us the area of the entire figure. So we have six square meters, plus nine square meters, plus 27, and we can solve that, six plus nine is 15, 15 plus 27, let's see, five ones and seven ones is 12 ones. We'll just find some space up there. And one 10 and two 10's or a 10 and a 20 is 30. And 30 plus 12 is 42. So the area of the entire figure is 42 square meters.