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

What is the area of the figure?

So down here we have this 10-sided figure, and we want to know its area. How many square meters does this figure cover? We have some measurements that seem helpful, but what's not too helpful to me is I don't know the special trick to find the area of a 10-sided figure.

So I've got to think about what I do know. What I do know is the way to find the area of a rectangle. What I can do is see if I can find any rectangles in here. Here's one rectangle right there. So I can find the area of that part.

Then let's see if I can find more. Here's another rectangle, so I can find the area of that part. We could call that one a rectangle or a square. And then that leaves us with this last part, which is again a rectangle.

So what we did is we broke this up or decomposed it into three rectangles. Now, if I find out how much space this purple one covers, the blue one, and the green one, if I combine those, that would tell me the area of the entire figure—how much space the entire figure covers.

So let's start with this one right here. This one is 3 m long, so we can kind of divide that by 3 m into three equal m. Then we got a width of 2 m down here, so let's put that in half.

If we draw those lines out, we can see this top row is going to cover 1 square m, 2 square m, 3 square m. And then there are two rows of that, so there's two rows of 3 square m, or a total of 6 square m. This rectangle covers 6 square m, so this part of the entire figure covers 6 square m.

The next one, our measurements are 3 and 3, so it will have three rows of 3 square m, or 9 square m. And then finally, this purple one has 3 m and 9 m, so we can say it will have three rows of 9, or 9 rows of 3 square m, which is 27 square m.

So the area of this purple section covers completely 27 square m. The green covers 9 square m, and the blue covered 6 square m. So if we combine all those areas, all those square meters it covers, that will tell us the area of the entire figure.

So we have 6 square m + 9 square m + 27 square m, and we can solve that. 6 + 9 is 15. 15 + 27, let's see, 5 plus 7 is 12. Just find some space up there: 110 and 2—10 or a 10 and a 20 is 30, and 30 + 12 is 42.

So the area of the entire figure is 42 square meters.