 Hi, this video is called Finding Perimeter and Area of Irregular Shapes. It is the first video for chapter 11 in section 11.1. If you look at this shape, you can definitely see that it's irregular. You can't really name that as a quadrilateral or a triangle or a square. I don't really know what it's called. So to find the perimeter, which will be the distance around and the area, the distance inside, we're going to have to do some work to break it up into familiar shapes that we can work with. Before I do that, though, let's fill in all the side lengths that we are missing. Okay? I see the left-hand side, a side length of three, all along the top, a side length of six. So all along the bottom, here, here, and here would have to add up to six. Well, since I have a side length of one, a side length of two, which is three, that gives me three left over to get to six. So the top length matches the bottom. Now let's do the same with the left and the right. The vertical length is three. So on the right-hand side, I've got a side length of one and a side length of one to add up to two. So that would make this missing one, I'm sorry, not a two, but a one. So the vertical lengths on the left can add up to three, so they match. Okay? So perimeter, then, will be fairly easy. All we have to do is add up all of those sides. So just be careful that you don't miss anything. So all I did here was I took all of my sides, starting at the top, going clockwise around six plus one, plus one, plus one, plus two, plus one, plus three, plus three, and that adds up to 18 units. Now in this chapter, labels are going to start mattering. If teachers haven't started docking points for mislabeling, they will start doing it this chapter. So start now, get in the habit. When you're finding perimeter, you'll always label it with units, meters, miles, centimeters, whatever it happens to be. All right, now let's move on to area. To find the area of an irregular shape like this, you have to break it down in a way that makes sense to you, in a way that gives you shapes that you do have formulas for. And the hard thing about this is in this shape, there's a lot of ways to break this up into shapes that we are familiar with. Let me try, show you one way you could do it. What I did here was I just drew two horizontal lines through my picture, which created three rectangles. Now I know how to find area of a rectangle very easily. It's just length times width or base times height. So let's go ahead and solve. If I start with my rectangle on the bottom, it looks like I have a base of three, a height of one. Three times one is three. If I look at the rectangle in the middle, it looks like I've got a base of three, four, five, and a height of one, five times one is five. Then my rectangle on the top has a base of six, a height of one, six times one is six. So I found the individual areas of each piece, now you add them up. Six plus five plus three gives me 14 units squared. So just like perimeter, you would label your answer with units. Anything that's area will be units squared. So it might be meters squared, feet squared, inches squared. If we don't specify, just use units or you. Now, very quickly, I just want to show you another way you could have broken up this shape that would have worked very well, is if you wanted to have drawn two vertical lines in, you would have created three rectangles or squares as well. So you would look at the rectangle on the left, the height is three, the base is three, three times three is nine. This shape in the middle, it looks like it has a base of two and a height of two, two times two is four. And this little square here, one times one is one. If you do nine plus four plus one, you'd also get 14 units squared. So you can see there's many ways to divide up these shapes to find the area. You just have to do it, be as simple as you can, and make shapes that you know formulas for, like rectangles and squares. Let's try another one. Here we go to find the perimeter and area of this shape. First perimeter, we have to just find the side lengths of everything that we're missing. So it looks like the vertical length is 10. So I have to make sure on the right-hand side, my vertical lengths add up to 10. Here I've got two, here I've got six, here I've got two again. So let's think about this. If I drew an imaginary line here, that would make this four. So I'd have two here, four here. So what would this have to be to add up to 10? It would have to be four as well. I'll erase this imaginary line. Looks like we've got a four down at the bottom. Right above it, we will have a four on top. And what other one are we missing? Oh, right down here in the middle along the bottom. It looks like on the top, we go 12 across. Then on the bottom, if this is six across, this will also be six across. So now I'm ready to find my perimeter. You just be careful. Make sure you don't miss any of the sides. All right, so I just made a list where I listed all of my sides. You should do the same thing. I started on the left-hand side with 10 and went clockwise around. So I had 10 plus four, sorry, 10 plus four, plus two, plus 12, plus six, plus six, plus two, plus six, plus four, plus four, that gave me 56 units. Don't forget your label of units, okay? Now let's go ahead and look at area. I already kind of drew one imaginary line in. I think I'll keep it there. And then I'm gonna do one more over here. So I've created three, it looks like two rectangles and a square. That should be pretty easy to find the area of each individual piece and then add them up. Let's start on the left-hand side. It looks like I have a rectangle that has a base of four and a height of 10, 10 times four is 40. So the area of the rectangle on the left is 40. The middle rectangle, it looks like it has a horizontal base of six, a vertical base height of four, six times four is 24. So the area inside that part of my shape is 24. And then to finish on the right, base of six, height of six, so this is a square, six times six is 36. So now all I have to do is add up these three sides to get my total area. 40 plus 24 plus 36. It looks like I get 100 and we would label that unit squared because we are finding area. So don't forget area, unit squared, perimeter, just units.