Decomposing shapes to find area (grids) | Math | 3rd grade | Khan Academy

Each small square in the diagram has a side length of one centimeter. So, what is the area of the figure? 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.

That means each of these squares is one square centimeter. We can find the area by seeing how many square centimeters this figure covers. One way would be just to 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 look at this and try to break it into two shapes. We can say down here into two rectangles. Down here, we have one rectangle, and up here, we have a second rectangle. 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 are two rows of seven unit squares or seven square centimeters. The bottom rectangle is made up of 14 square centimeters. It covers 14 square centimeters.

Now, for 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. 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. Thus, 24 square centimeters is our area, because area is how much space it covers, and we figured out that it covered 24 square centimeters.