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

What is the area of the shaded figure? So down here we have this green shaded figure, and it looks like a rectangle, except it has this square cut out in the middle.

So when we find its area, we can think of it exactly like that. We want to know how much space it covers; it covers this rectangle's amount of area with this square cut out.

So what we can do is find the area of the larger rectangle and then cut out or subtract the area of the square to see what's left in this shaded area.

So let's start by finding the area of this larger rectangle, and to do that we can look at the side lengths. It has side lengths of 9 and 8. To find the area of a rectangle, we can multiply the side lengths. So 9 times 8 is 72.

That means that this rectangle covers 72 square centimeters. This entire rectangular area covers 72 square centimeters. But now we need to cut out or subtract the area of this square because that's not part of our shaded figure. We need to cut that part out.

So to do that, we know the side lengths are four on the square. So we can think of this as four centimeters across. So we can divide it into four equal sections, and same going this way.

And then, if we connect these lines, what it will show us is that we have—it's not drawn perfect—but we have four rows of four square centimeters. Four times, we see four square centimeters. This top row: one, two, three, four, and so on, four rows.

So there are 16 square centimeters we need to cut out of the 72 of this entire rectangular area. We need to cut out or subtract 16 of these square centimeters.

So let's do that. We have 72 as the entire area, and then let's start subtracting. I subtract out 10 of them just because, for me, I like subtracting 10s because they're simpler.

So 4, 8, 10 of the square centimeters. Now we're down to an area of 62 left. And then, let's subtract those two more; it will get us to—subtract two more will get us to sixty.

And then there's four left to subtract in order to subtract all 16. So 60 minus four gets us to 56.

So the entire area of 72, we subtracted out these 16 square centimeters, leaves us with a final area of 56 square centimeters.