 In this video, I'm going to talk about area and perimeter as it pertains to geometry. So this is just a couple area and perimeter examples I'm going to go through. Now, at this point, I'm assuming that we do know what area and perimeter are and how they pertain to either triangles, rectangles, squares, and even circles. I don't think I have any circle examples here, but let's go ahead and get started. I'll find the perimeter, find the perimeter, and the area of a rectangle with a length. Now, L sometimes they look like ones, so this is a nitrolyzed L. Length is 15, L is equal to 15, and W is equal to 7. The width is 7 inches. So now the thing is, this is the rectangle. So what I'm going to do is I'm going to draw myself a simple little picture of what a rectangle is. I've got a length of 15 inches and I have a width of 7 inches. So right there, that gives me an idea of what this looks like. It gives me an idea of what this looks like. This helps me because then what I can do is when I find the perimeter and when I find the area, I can take these numbers set 15 and 7, do I add them, multiply them, subtract them, divide them. What do I do with them? It just helps me out a little bit. All right, so the perimeter, what I'm going to do first is I'm actually going to use the formulas. I don't really like using the formulas for perimeter and area. I just like to either multiply or add whatever it is that I need to do. But for the sake of these examples, I will use the formulas. So in this case, perimeter is equal to 2L plus 2W. Now notice the L as I tele-sized for the problem, but my L that I draw is cursive. Cursive L is very much distinguished, different from a 1, so it helps us out a little bit. Anyway, so the perimeter of a rectangle is twice the length plus twice the width. So in this case, perimeter is going to be equal to 2 of the lengths. You have 2 lengths, which is 15 plus 2 of the widths. Width is 7, so 2 of the lengths is 30 plus 2 of the widths is 14. So my perimeter in this case is going to be 44 inches. Don't forget your label there. Now in the past, I said make sure to actually answer the question. In this case, if you use a capital P is equal to 44 inches. Capital P is commonly referred to as perimeter in most every mathematics book anywhere you go. So this is okay to use capital P for perimeter. That's okay to use because that's commonly what they use for perimeter, what everybody uses for perimeter. Okay, so now that we've got perimeter, now let's do area. So the area of a rectangle, area is simply length times width. So I just take the two dimensions, length is a dimension, width is a dimension. Take the two dimensions and multiply them together. So in this case, area is equal to, use your parentheses here, 15 times 7. So area in this case, let's see if I can do this in my head. 10 times 7 is 70, and 5 times 7 is 35. So 70 and 35 make 105. So my area is 105 inches squared or square inches. Make sure you distinguish, okay, let me emphasize this here. Make sure you distinguish the difference between area, area, which is square inches, and perimeter, which is just inches. Okay, make sure you distinguish the difference between the two. If you don't put that label there, that doesn't mean you understand the dimensions. Area is the space inside the rectangle, perimeter is the space around it. So put this a little bit more practically, a little bit of a practical example. Area, you can think, okay, if this is a yard, this is your front yard. Very small, 15 by 7 front yard. But if this is a yard, the area is the grass that's going to be inside of this yard. Okay, that's what area is. That's why you use square inches, two dimensions here. Perimeter, on the other hand, is going to be the fence that is around the yard. Perimeter is the fence around the yard. Make sure that you use the correct label so you tell me or tell your teachers the correct labeling between inches and inches squared. So you tell them you know the difference between perimeters and areas. Okay, enough of that. On to the next problem, on to this next one. Find the perimeter, find the perimeter and area of the following figure. You look at this following figure, what is it? It is a triangle. One thing that I believe is missing here, one thing that I believe is missing is that this is actually supposed to be a right triangle. I'm going to be very picky with that. This is going to be a right triangle because we can only use our formulas with a right triangle for now. Later on in mathematics, you'll use formulas. You'll use formulas that you don't have to have a right triangle, but you'll get there. Alright, find the perimeter in the area. Actually, I'm going to do area first. It doesn't really matter which one you do first. Green is a horrible color, by the way. Green with a white background is a horrible color. Let's just use black since that's what I have handy. The area is equal to... This is a triangle. Area is equal to one-half base times height. One-half base times height. Again, a little bit of vocabulary. You've got to know what the base is. The base in this case is going to be 6, and the height is going to be x plus 4. That's a little bit confusing. Why do we have a variable here? We have a variable 5y. We have a variable here. That's okay. Don't worry about it. Just plug in everything that you know. Get it a little bit lengthy here. Area is equal to one-half of the base, which is 6, times the height, which is x plus 4. What we're going to do is we're going to take this and we're going to simplify it. I've got a lot of things I can multiply together. I'm simply just going to simplify this. One thing I know is that half of 6, I actually know what that is. That's going to be 3. I just multiplied there. Half of 6 is 3. Another thing that I can do, since I'm going to use distributive property, is take 3 times x and 3 times 4. My area is equal to 3x plus 12. Do I have a label? Do I have a label? Do I have a label? No, I don't. I'm going to put units squared. My area is 3x plus 12 units squared. Again, it's a little bit confusing because normally in mathematics, normally for students, it makes neat number answers. Well, not really anymore. If you have variable answers, if you have x plus 4, you've got that 5x there, sometimes you're not going to get a nice easy answer. Sometimes you're going to get something like this, which is okay, but if you ever figure out what x is going to be or is supposed to be, then you can plug it in and very quickly find out what the area is going to be. I do a quick different color here. What I'm going to do is now I'm going to do the perimeter. Again, kind of doing this backwards. So perimeter, in this case, perimeter for any object is you just add up all the sides. The perimeter of a triangle is you just add up all the sides. Now I believe the formula that you write down for many of your books is going to be a plus b plus c, where a, b, and c are the three different sides of the triangle. I mean, you don't really need to write that down, but I think it's handy to have so that we can see what we're plugging in. So the perimeter of a triangle is going to be, I don't know what to do. This one is a, this one is b, this one is c here. So 6 plus x plus 4 plus 5x. So again, we got a lot of variables in there, but it doesn't really matter. We don't know what x is, nor do we have enough information to find out what x is. So we're just going to, we're just going to leave it. We're just going to add these things together. So I run out of room here on the bottom, go over here to the side. Perimeter is equal to, let's take the x's out of them together. I have 6x's and I have 6 and 4, excuse me, make 10. So 6x plus 10 units, units is my perimeter. Okay, and there we go. So again, sometimes you're not going to be able to get a nice, neat, clean answer, but that's okay. This kind of shows you the difference between a nice, neat, clean answer like we got over here with the rectangle and then some kind of messy answers where actually we got variables in there and we don't know all of the information. All right, so hopefully that gives you, it gives you some hints, gives you some tactics and strategies to help you with finding the area and perimeter of these different shapes. Again, one thing to reiterate, make sure your units with perimeter, it's always inches or meters or miles, whatever it is, and then with area, you're always inches squared, square miles, square meters, square kilometers, whatever it's going to be. Okay, make sure you know the difference between the two and even if you don't have any labeling, didn't have any labeling over here, that's okay, but put in your units. Area is going to be whatever units you're using squared. Perimeter is going to be whatever your units you're using. Okay, make sure you put that in so that you tell either myself or your teacher that you know the difference between area and perimeter. Labeling is very important for these type of problems. Hopefully that helps and that's my video on area and perimeter.