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# Perimeter & area

## Video transcript

what I want to do in this video is a fairly straightforward primer on perimeter and area perimeter and I'll do perimeter here on the left and I'll do area here on the right and you're probably pretty familiar with these concepts but we'll revisit it just in case you are not perimeter is essentially the distance to go around something or if you were to put a fence around something if you were to measure if you were to if you were to put a tape around a figure how long that tape would be so for example let's say I have a rectangle let's say I have a rectangle and a rectangle is a figure that has four sides and four right angles so this is a rectangle right here I have one two three four right angles and it has four sides and the opposite sides are equal in length so that side is going to be equal in length to that side and that side is equal to length to that side and maybe I'll label the points a b c and d and let's say we know the following we know that a b is equal to seven and we know that bc we know that bc is equal to 5 and we want to know what is the perimeter of ABCD so let me write down the perimeter perimeter of rectangle a b c d is just going to be equal to the sum of the lengths of the sides if i were to build a fence this was like a a plot of land i would just have to measure how long is this side right over here well we already know that's seven in this color so it's that side right over there is of length seven so it'll be seven plus this length over here which is going to be five they tell us that bc is five plus five plus DC is going to be the same length as a b which is going to be seven again so plus seven and then finally da or a d however you want to call it it's going to be the same length as bc which is five again so plus five again so you have 7 plus 5 is 12 plus 7 plus 5 is 12 again so you're going to have an area perimeter you're going to have a perimeter of 24 and you could go the other way around let's say that you have a let's say that you have a square which is a special case of a rectangle a square has four four sides and four right angles and all of the sides are equal so let me draw a square here so let me draw a square my best attempt so this is a B C D and we're going to tell us tell ourselves that this right here is a square and let's say that this Square has a perimeter so square has a perimeter perimeter of 36 so given that what is the length of each of the sides well all the sides are going to have the same length let's call them X so if that if a B is X then VC is X then DC is X and ad is X all of the sides are congruent all of these segments are congruent they all have the same measure we call that X so if we want to figure out the perimeter here it'll just be X plus X plus X plus X or for X let me write that X plus X plus X plus X which is equal to 4x which is going to be equal to 36 that gave us that in the problem and to solve this for x something is 36 you could solve that probably in your head but we could divide both sides by 4 and you get X is equal to 9 X is equal to 9 so this is a 9 by 9 square this this width is 9 this is 9 and then the height right over here is also 9 so that is perimeter area is kind of a measure of how much how much space does this thing take up in two dimensions and one way to think about area is if I have a if I have a 1 by 1 square so this is a 1 by 1 square and i'ts when I say 1 by what it means you only have to specify two dimensions for a square a rectangle because the other two are going to be the same so for example you could call this a 5x7 rectangle because that immediately tells you okay this side is 5 and that side is 5 this side is 7 and that side is 7 and 4 square you could say it's a 1x1 square because that specifies all of the sides you could really say for a square square where on one side is one then really all the sides are going to be one so this is a one by one one by one square and so you can view the area of any figure as how many 1 by 1 squares can you fit on that figure so for example if we were going back to this this rectangle right here and I want to find out the area of this rectangle and the notation we can use for area is put something in brackets so the area of rectangle ABCD a b c d is equal to the number of 1 by 1 squares we can fit on this rectangle so let's try to do that just manually I think you already might get a sense of how to do it a little bit quicker but let's put a bunch of one by one so let's see we have 5 1 by 1 squares this way and 7 this way so I'm gonna try my best to draw it neatly so that's 1 2 3 4 5 6 and then 7 1 2 3 4 5 6 7 so going along one of the sides if we just go along one of the sides like this you could put seven just along one side just like that and then over here how many can we to see we see that's one row that's two rows two rows then we have three rows and then four rows and then five rows 1 2 3 4 5 and that makes sense because this is 1 1 1 1 1 should add up to 5 these are 1 1 1 1 1 1 1 should add up to 7 yep they're 7 so this is 5 by 7 and then you could actually count these and this is kind of straightforward multiplication if you wanted to know the total number of cubes here you could count it or you'd say well look I 5 rows 7 columns I'm going to have 35 not adjusted cube squares I have 5 squares in this direction 7 in this direction so I'm going to have 35 total squares so the area of this figure right over here is is 35 and so the general method you could just say well I'm just going to take one of the dimensions and multiply it by the other dimension so if I have so if I have a if I have a rectangle let's say the rectangle is 1/2 by 1/2 by 2 those are its dimensions well you can just multiply it you say 1/2 times 2 the area here is going to be 1 and you might tell me what is 1/2 mean what means in this dimension I can only fit half I can only fit half of a I can only fit half of a 1x1 square so if I want to do the whole 1 by 1 square it's a little distorted here it would look like that so I'm only doing half of one I'm doing another half of one just like that and so this when you add this guy and this guy together you are going to get a whole one now what about area of a square well the square is just a special case where the length and the width are the same so if I have a square let me draw a square here and let's call that X Y Z I don't know let's make this s and let's say I wanted to find the area and let's say I know one side over here is 2 so X s is equal to 2 and I want to find the area of X Y Z s so once again I use the brackets to specify the area of this of this figure of this polygon right here the square and we know it's a square we know all the sides are equal well it's a special case of a rectangle where we would multiply the length times the width we know that they're the same thing if this is 2 then this is going to be 2 so you just multiply 2 times 2 or if you want to think of it you square it which is where the word comes from squaring something so you multiply 2 times 2 2 times 2 which is equal to 2 squared that's where the word comes from finding the area of a square which is equal to which is equal to 4 and you can see that you can easily fit you could easily fit 4 1 by 1 squares on this 2 by 2 square