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Finding area by rearranging parts

Discover the magic of quadrilaterals and their areas! We explore how a trapezoid's area can match a rectangle's by rearranging its parts. We learn that shapes with the same area can look different. It's a fantastic journey into the world of geometry! Created by Sal Khan.

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Video transcript

- [Instructor] We have four quadrilaterals drawn right over here. And what I want us to think about, is looking at this green quadrilateral here, I want you to pause the video and think about which of these figures have the same area as the green quadrilateral. And so pause the video now and think about that. So I'm assuming you gave a shot at it. Now let's think about it. And the way I'm gonna think about it is to really rearrange parts of this green quadrilateral to make it look more like maybe some of these other quadrilaterals. So for example, if we were to put a little dotted line right over here and a dotted line right over here, we see that our green shape is actually made up, you could imagine it being made up of a triangle, and then a rectangle, and then another triangle. And what's interesting about the two triangles is that they represent the exact same area. They essentially each represent half of this rectangle right over here. They represent half of this rectangle down here. Let me do that in a color. They represent half of this entire thing. If I were to color it all in. And if you have trouble visualizing it, imagine taking this top part right over here and then flipping it over, it would look like this. If you flip it over this line right over here, it would look something like this. It would look something like this. My best attempt to draw it. So take that top section, it would look something like that, and then move it down and then move it down right over here to fit in here. And then this, plus this will fill in this entire region right over here. So that original green trapezoid that we were looking at, if you take that top part out, it essentially has the exact same area as a rectangle that has a height of four and a length of five. So this right over here has the exact same area as our trapezoid. And once again, how did we do that? Well, we just took this top part, flipped it over, and relocated it down here, and we said, hey, we could actually construct a rectangle that way. So essentially, and if you wanna know its area, we could either just count the squares here. So we have, let me do this in a easier to see. So we have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 of these unit squares right over here. And we know that there's an easier way to do that. We could have just multiplied the height times the width. We could have just said, look, this thing is 1, 2, 3, 4 high and 1, 2, 3, 4, 5 wide. So four times five is gonna give us 20 of these unit squares. So that's the area in terms of unit squares or square units of that original green trapezoid. Now let's see which one of these match that. So this pink one right over here, if you don't even count this bottom part, if you were to just separate this top part right over here, this top part is four high by five wide. So just this top part alone is 20. And then it has this extra right over here. So the pink has a larger area than our original green trapezoid. The blue rectangle is three by five. So it has an area of 15 square units. Now the red one is interesting. It is 1, 2, 3, 4 high and 1, 2, 3, 4, 5 long or five wide. Four times five is 20 squares. And you can validate that. And so the red rectangle has the same area as our original green trapezoid.