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Decomposing shapes to find area: grids

Lindsay finds the area of an irregular shape by decomposing it into 2 rectangles.  Created by Lindsay Spears.

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    • male robot johnny style avatar for user 🅹🅾🅷🅽🅽🆈
      This could be useful to many job purposes. One example is being an architect. Suppose you need to design a house for efficiency and low cost. Part of the house that you are building might be in an irregular shape style. You would have to know the area of it because it could help you put things like a bed inside. If you just randomly make a house with no blueprints or area models, you definitely would mess up. You could make a room too small or forget to place a door. There are many more ways that math can help us in our life, but this is just one of them. Hope this helped! -Johnny Unidas
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Video transcript

- [Voiceover] Each small square in the diagram has a side length of one centimeter. So, what is the area of the figure? So, we have this figure down here in blue, and we want to know its area. Area is the total space it covers. And, we're also told that each of these little squares has a side length of one centimeter. So, that means that each of these squares is one square centimeter. So, we can find the area by seeing how many square centimeters does this figure cover? One way would be to just try to draw the little square centimeters and count them. There's one square centimeter, there's two, and so on and keep counting them all the way through. Or, what we could do is we could look at this and try to break it into two shapes. So we can say down here, into two rectangles. Down here we have one rectangle, and up here we have a second rectangle. And then we can find the area of each rectangle and add it together to find the total area that the figure covers. Down here on the bottom, we have two rows of unit squares. And each of those has one, two, three, four, five, six, seven. So, one, two, three, four, five, six, seven. So there's two rows of seven unit squares, or seven square centimeters, so the bottom rectangle is made up of 14 square centimeters. It covers 14 square centimeters. And the top rectangle, let's see we have one row, two, three, four, five rows. And each of those rows has one, two square centimeters, so we have five rows of two square centimeters, or 10. So, this top rectangle here that we have in blue covers 10 square centimeters, plus the bottom rectangle that we outlined in green covers 14 square centimeters, so in total, the entire figure covers 24 square centimeters. So, 24 square centimeters is our area, because area is how much space does it cover, and we figured out that it covered 24 square centimeters.