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Measuring area with partial unit squares

Lindsay finds the area of a shape by counting whole and partial unit squares.  Created by Lindsay Spears.

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Video transcript

- [Voiceover] Each square on the a grid is unit square with an area of one square centimeter. So each of these squares is one square centimeter. This is one square centimeter, and this is one square centimeter, and so on. And now we're asked, what is the area of the figure? By figure I'm sue they mean this bluish, purplish quadrilateral, and we wanna know its area. And area is talking about how much space the shape covers. How much space does this quadrilateral cover? How many square centimeters does the quadrilateral cover? To figure it out, we could start by counting. Here's one. Here's one square centimeter the quadrilateral covers, and I can keep counting like that, all of the square centimeters that I can see. Here's two, three. Another row's got some here. Four, five, six. Down here, here's seven. Eight, nine. So there's nine full square centimeters. Nine square centimeters, but that's not the entire area. That's not everything it covers. It also covers these small parts, these triangle-shaped little spaces of area, and so we need to count those too. Let's look over here. Let's look, if we drew one of these triangles into a unit square, and then we drew another one on the other half of this unit square, we would see that combined they make one full unit square. So we can do that. We can take this triangle up here, which is half of a unit square and combine it with this half of a unit square. So if we combine these two together, that's one more unit square. Now we have nine full unit squares plus one more. But there's still more of them, so we can keep combining. This half unit square combined with the other one on the bottom makes a second unit square, and finally, there's two more halves here, one, two, which combine to make another whole. So we have nine full unit squares plus, plus three more unit squares that we made by combining. We made one by combining these two, a second unit square with these two, and a third unit square here. So we have nine full unit squares and then three more unit squares we put together, which is a total of 12 square units or 12 square, in this case our unit is centimeters, 12 square centimeters. Our figure, our quadrilateral covers 12 square centimeters, so it has an area of 12 square centimeters.