Area of a quadrilateral on a grid

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 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 points where it would be very easy to measure the dimensions of whatever figures we might break it up at. And so in general, I want to go to any of the whole numbers of these units, so that point right over there. And let's see. 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 halfway through a unit. And I'm just eyeballing it to say halfway through a unit. 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 make another triangle where it 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 whole unit. Instead, let me take a right and go right over here. And notice, both of these are 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 long and 1, 2 units wide. So let's see if we can cover the entire quadrilateral, if 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 2. This is 1, 2, 3, 4, 5, 6 by 1, 2. And this is 1 by 1, 2, 3, 4, 5. So what is the area of this figure? And of course, we have this center rectangle right over here. Well, a triangle that is 5 units long and 1 unit high, its 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 half times 2 is 1 times 6 is just 6. And then this one's 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 could even count the unit squares in here. But it has 12 of those unit square, 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.