Finding area by rearranging parts

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 going to think about 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 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 both represent, they each represent half of this rectangle right over 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. My best attempt to draw it. So take that top section, it would look something like that. 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 4 and a length of 5. 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 want to know its area, we could either just count the squares here. So we have, let me do this in an 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 4 times 5 is going to give us 20 of these units 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 4 high by 5 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 3 by 5. 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 5 wide. 4 times 5 is 20 squares, and you can validate that. And so the red rectangle has the same area as our original green trapezoid.