Measuring area with partial unit squares | Math | 3rd grade | Khan Academy

Each square in the grid is a unit square with an area of 1 square cm. So, each of these squares is 1 square cm. This is 1 square cm, and this is 1 square cm, and so on. Now we're asked, what is the area of the figure? By figure, I'm sure they mean this bluish purplish quadrilateral, and we want to know its area.

Area is talking about how much space the shape covers. How much space does this quadrilateral cover? How many square cm does the quadrilateral cover? To figure it out, we could start by counting. Here's one; here's one square cm the quadrilateral covers. I can keep counting like that all of the square cm that I can see.

Here's two, three. Another row's got some here; four, five, six down here. Here's seven, eight. So, there's nine full square cm. Nine square cm, 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, which makes a second unit square.

Finally, there's two more halves here, one, two, which combine to make another whole. So we have nine full unit squares 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 cm. In this case, our unit is cm². Twelve square cm. Our figure, our quadrilateral, covers 12 square cm, so it has an area of 12 square cm.