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Current time:0:00Total duration:3:54

Video transcript

I want you to pause this video and figure out if you can figure out the area of this quadrilateral right over here and I'll give you a hint try to break it up into into shapes where it is easier to find the area especially given the grid of these unit squares that we have right over here so I assume you gave it a go now let's try to do it together so I'm going to start at at points where we would be very easy to measure very easy to measure the the dimensions of whatever figures we might break it up at it so in general I want to go to any of the whole numbers of these of these units so that point right over there and let's see I could start to move in this direction I could start to move in this direction and it looks like I might be able to construct a triangle down here and it would be tempting to go all the way across but that wouldn't be too useful because this gets me to kind of halfway through a unit and I'm just eyeballing it to say half way three and it might not be exactly halfway through a unit and so instead let me see if I can get away with making a triangle just like that now I just did that so let me try to raise this up to see if I can if I can make another triangle would be easy to figure out its dimensions so once again I don't want to go all the way up here because now I'm not at a at kind of a whole unit instead let me take a right and go right over here and all of these are pretty easy or they're very easy to figure out its dimensions this is 1 2 3 4 5 units long and 1 unit high this one right over here is 1 2 3 4 units high and 2 or 4 units long and 1 to 2 units wide so let's see if we can if we can map out the entire if we can cover the entire square or the entire quadrilateral we can break it up I should say into a bunch of figures like this so it seems like we have another one just like that and then I could drop this down and then we're done all of these are pretty straightforward to figure out what their dimensions are this is 5 by 1 this is 4 by - this is 1 2 3 4 5 6 by 1 2 and this is 1 by 1 2 3 4 5 so what are what is the area of this figure and of course we have the center rectangle right over here well a triangle that is 5 units long and 1 unit high it's area is going to be 1/2 times 1 times 5 or I could write it 1/2 times 1 times 5 depending on what multiplication symbol you are more comfortable with well that's just going to be 1/2 times 5 which is going to be equal to 2.5 so that's 2.5 right over there this one is going to be 1/2 times 4 times 2 well that's just going to be 2 times 2 or 4 this one is going to be 1/2 times 2 times 1 2 3 4 5 6 well 1/2 times 2 is 1 times 6 is just 6 and then this was going to be 1/2 times 1 times 1 2 3 4 5 so once again the area of this one is going to be 2.5 and then finally this is a 3 by 4 rectangle and you can even count the unit squares in here but it has 12 of those units squared so it has an area of 12 so if we want to find the total area we just add all of these together so 2.5 plus 2.5 is 5 plus 4 is 9 plus 6 is 15 plus 12 is 27 so it has a total area of 27