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# Comparing areas and perimeters of rectangles

CCSS.Math:

## Video transcript

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 were 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 and 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 in 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 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 length or dimes 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 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 move rectangle but we need to figure out its area in order to figure out the 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 so what would it be the distance of this side this side our length Plus this side well it would be half the perimeter five plus something is going to be equal to half the perimeter over 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 five plus what is equal to 17 five plus this question mark is equal to 17 well five plus 12 is equal to 17 and you can verify this 12 plus 5 is 17 and then that times two gets us the perimeter of 34 now given that what is the area of this figure well the area is going to be twelve units times five units to get sixty square units area is equal to sixty so this one right over here has the same area different perimeter same area as the original as the original yellow rectangle different area now let's go over here so I have and 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 eight units times eight units is 64 square units and what is the perimeter here what is the perimeter 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 eight and this is also eight so the perimeter is eight times four eight times four 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 as our original yellow square now let's move on to this blue one what's the area and you're probably getting used to this 15 units times four 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 20 square 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 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 this one's perimeter looks just like the same it's the same numbered 60 as the area here but that's not what we're comparing we have a different perimeter and different areas so neither of these are the same as our original rectangle