Sal compares the areas and perimeters of rectangles to a given rectangle. Created by Sal Khan.
So I have this yellow rectangle here, and we know two things about this yellow rectangle. We know that it has a length of 10, that the length of this side right over here is 10. And we also know that this yellow rectangle has an area of 60 square units, whatever units we're measuring this 10 in. So what I want you to do is now pause this video, and based on the information given on these other rectangles-- so in some of them we give you two of their dimensions, in some of them we give you something like the perimeter and one of the dimensions-- I want you to pause the video and think about which of these rectangles, if any of them, have either the same area or the same perimeter as this yellow rectangle. So pause the video right now. Well, the best way to figure out which of these have the same area or perimeter as this original yellow rectangle is to just figure out the area and the perimeter for all of these rectangles and see which ones of them are equivalent. So we already know the area for this one, but we don't know its perimeter. So how do we figure that out? Well, to figure out perimeter, we would need to know the lengths of all the sides. Well, if the area is 60 square units, that means the length times the width is equal to 60, that 10 times this width right over here is going to be equal to 60. So 10 times what is equal to 60? Well, 10 times 6 is equal to 60. 10 times 6 is equal to 60 square units. 10 units times 6 units is equal to 60 square units. Fair enough. So how do we figure out the perimeter now? Well, this is a rectangle. So we know if this length is 10, then this length must also be 10. And if this width is 6, then this width must be 6 as well. And now we can figure out the perimeter. It's 10 plus 10 plus 6 plus 6, which is 32. So let me write that down. The perimeter of our original yellow rectangle is equal to 32. Now let's go on to each of these other rectangles and figure out what their perimeters and the areas are. We already know the perimeter for this purple or mauve rectangle, but we need to figure out its area. In order to figure out its area, we can't just rely on this one dimension just on its width. We have to figure out its length as well. So how do we figure that out? Well, one way to realize it is that the perimeter is the distance all the way around the rectangle. So what would be the distance halfway around the rectangle? So let me see if I can draw it. What would be the distance of this side, our length, plus this side? Well, it would be half the perimeter. 5 plus something is going to be equal to half the perimeter. Remember, the perimeter is all four sides. If we just took these two sides, which would be half the perimeter. So, these two sides must be equal to, when you take their sum, must be equal to 17, half the perimeter. So 5 plus what is equal to 17? 5 plus this question mark is equal to 17. Well, 5 plus 12 is equal to 17. And you can verify this. 12 plus 5 is 17, and then that times 2 gets us the perimeter of 34. Now, given that, what is the area of this figure? Well, the area's going to be 12 units times 5 units to get 60 square units. Area is equal to 60. So this one right over here has the same area, different perimeter. Same area as the original yellow rectangle, different area. Now let's go over here. So this is not just a rectangle. This is also a square, because I have the same length and the same width. So what's the area here? Well, for the area, I just have to multiply the length times the width. 8 units times 8 units is 64 square units. And what is the perimeter here? Well, these two sides are going to make up half the perimeter. If I wanted to figure out the whole one, I know this is also 8 and this is also 8. So the perimeter is 8 times 4. 8 times 4 sides, which is equal to 32. So this square right over here has a different area, but it has the same perimeter as our original yellow square. Now let's move onto this blue one. What's the area? And you're probably getting used to this. 15 units times 4 units is going to be 60 square units. And what's the perimeter? What's the perimeter? Well, it's going to be 4 plus 15, and whatever that is times 2. 4 plus 15 is 19. And then 19 times 2 is 38. So this one right here has the same area, different perimeter as our original. Now, finally, here in purple, what is the area? The area is 10 times 20, which is equal to 200. So if it's 10, say, well, 10 units times 20 units is 200 square units. And what is the perimeter? What is the perimeter? Well, 10 plus 20 is 30, but I've just considered only two of the sides right here. That's only half way around. So 10 plus 20 is 30 times 2 is 60. So let's see. This has a different area, and it also has a different perimeter. This one's perimeter looks just like the same number. It's 60, as is the area here, but that's not what we're comparing. We have a different perimeter and different area. So neither of these are the same as our original rectangle.