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 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 if we were to put a little dotted line right over here and a dotted line right over here we see that our green 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 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 I would 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 this entire region right over here so that original green trapezoid that we were looking at if you take the top if you take that top part out it essentially has the exact same area as a rectangle as a rectangle that has a height of four and a length 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 flip it over and relocated it down here and we say hey we could actually construct a rectangle that way so essentially and and if you want to 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 hi and 1 2 3 4 5 wide so 4 times 5 is going to 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 4 high by 5 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 a an area of 15 square units now the red one is interesting it is 1 2 3 4 hi 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