Notes 1.7 Perimeter and Area

[00:00:00]hello everybody and today we're going to talk about notes 1.7 which is on perimeter and area in this section we're going to review some formulas for perimeter area and circumference so right off the bat here i've got you all the formulas for the different shapes we're going to be looking at in this section here so we've got formulas for the perimeter area and circumference of some of the common figures below so we have the square and its side length is s because they're all the same and the perimeter would be just four times s because it's the same thing as adding all four of them the area is the side squared then we have the triangle with side lengths a b and c a base of b and a height h so if we want to find the perimeter of course we just add the sides a plus b plus c if we want to find the area that's one half the base times the height on the top right i have the rectangle with its length l and width w the perimeter is 2l plus 2w because we of course have two lengths and two widths and the area is just the length times the width and then we have the circle with the radius of r now circumference is just you can almost think of it as another word for uh perimeter it's just that we don't really talk about a circle having a perimeter because uh when we talk perimeter we usually talk about adding the sides and a circle has no sides so it gets its own word which is circumference which is just the the distance around the circle of course so it's 2 times pi times r now one quick note here and i'll make that note again later when you use pi in your calculations you want to use 3.14 because of how it's learning grades so use 3.14 for your pi values and then of course we have the area equals pi r squared all right and then we there we have a little note that pi is the ratio of the circle circumference to its diameter all right so let's go in to some examples down here first off we're going to start off with some square examples so my first example here in example 1a i want to find the perimeter of the square whose side is 32.7 so i just want to go ahead and get my perimeter of square formula so my perimeter is equal to 4 times s and they gave us what the s value is is that 32.7 so the perimeter is going to equal 4 times that 32.7 feet and i'm going to go ahead and do this and then i'm going to say the perimeter is then when i do that calculation it's going to be 130.8 feet now when you do your calculations and your answers on its learning you won't actually need to put the feed in there you can just enter the numerical value so you'll just be entering the 130.8 so that way you don't get any mistakes okay part b is a very similar example with a different number let's go on to example two so it says the perimeter of a square is 68.8 inches find the length of the side of the square so again this is kind of a problem that works backwards we could understand the perimeter is equal to 4 times the side and then they gave us the perimeter so we could say that 68.8 is what p is and it's an inches so we can say 68.8 inches is equal to four times s and then we can go ahead and divide both sides by four to figure out the side length is 17.2 inches again just a brief reminder that you will not need to enter the label you will not need to enter inches into its learning all right let's go to another example let's look at example 3.

[00:03:16]i want to find the area of the square with a side length of 6.2 so again we just grab our area of square formula which is that's the area is equal to s squared or maybe if you don't have a calculator it has a squared feature then you could also say that you're just doing the area is the side times the side all right but in any case we're going to go ahead and say the side length is 6.2 so it's going to be 6.2 centimeters squared and what's going to happen here is we're going to type in 6.2 squared on our calculator we'll get 38.44 now label is also getting squared so the answer here is going to be in centimeters squared all right so we get 38.44 centimeters squared for your area all right let's go through and look at example 4a the perimeter of a square is 32.4 millimeters find the area of the square so this one's going to ask you to kind of combine both formulas and figure out what the area is so we start off with what we know the perimeter is 32.4 so we can see the perimeter is four times the side length and we know that this is 32.4 and we can go ahead and say that's millimeters is equal to four times the side length and if we solve for that side length by dividing by 4 and figure out that s is equal to 8.1 millimeters okay so what we want to do with that is we're going to go ahead and say okay well we're trying to find the area and we know the area is equal to the side squared and so now that we have the side length which is 8.1 millimeters we can say this is 8.1 millimeters squared and type that in our calculator and figure out that the area is 65.61 millimeters squared all right so there are some square examples for you let's move on to our actually let's go through some rectangle examples so with example five we have find the perimeter of a door that's 7.4 feet tall and 3.4 feet wide so they're just kind of trying to tell you this is the length and of course this is the width okay we're trying to find the perimeter of this door so we know the perimeter is equal to 2 times the length plus 2 times the width and well now we just need to plug in our information so perimeter is equal to 2 times 7.4 feet plus three point five sorry two times three point five feet and if we calculate those then we can say this is going to be two uh well if i multiply it excuse me then we're going to get our 14.8 feet plus seven feet you notice these labels are the same they're both feet so i can successfully add these to get 21.8 feet all right let's go on to example six we have find the area of a door that is 7.4 feet tall and 3.5 feet wide so again they're telling you the length and the width right out of the problem there and we know that area of rectangle is given by the length times the width and so if we just go through and calculate this we can say it's 7.4 feet times our 3.5 feet and the calculation the 7.4 times the 3.5 we would get 29.5 and the labels there again we're multiplying feet times feet so we'd be getting feet squared all right just a reminder though again you will not need to enter these labels on its learning so you'll just be entering the 29.5 all right let's keep going with example seven who says the perimeter of a pool is 116 meters and the width is eight meters find the length of the pool all right so again they kind of gave us a couple of pieces of information here they gave us the perimeter and they gave us the width and we're trying to find the length so we know that we need the perimeter formula 2 length plus 2 w and then we can plug in what we know we know the perimeter is 116 meters so 116 meters is equal to i believe this is l 2 times l plus 2 times 8 meters it's an m there sorry i can fix that for you guys all right and uh then we can go ahead and do some some simplification here 116 meters equal to 2l plus 16 meters and of course i'm just trying to isolate the l get the l by itself here so i'm going to subtract 16 on both sides i have 100 meters is equal to 2l and then i can divide by 2 on both sides and figure out that l is equal to 50 meters all right so you can example eight it says the area of rectangle is 40.18 inches squared and the width is 4.9 inches find the perimeter of the rectangle so again we just have to go with what we know and and try to figure out where we need to go so we know that the area is 40.18 so we can go ahead and say i want to involve my area formula which i know is length times width and i know the area is 40.18 inches squared and i can set that equal to the length that i don't know times the width that we do know which is i'm going to put in parenthesis 4.9 inches the length times the width there and we're going to divide both sides by 4.9 here so if i divide both sides by 4.9 i would end up with 8.2 okay now watch the label here okay so as we divide in inches over we're actually gonna have this case we'd have like an inches squared over inches so if you guys remember from your algebra days you'd like cancel out inches in both places so you just end up with inches which makes sense because the length of the side should be measured in inches so this is good all right then we need to find the actual perimeter here so we're going to say the perimeter is equal to the 2 times the length plus 2 times the width and we can actually plug in everything that we have now so we say that that's 2 times 8.2 inches plus 2 times 4.9 inches and if you go through and calculate this you'll figure out the perimeter is equal to 26.2 inches all right let's talk about this triangle all right so we want to find the perimeter and area of this triangle that i have drawn over here to the right so first of all the perimeter of a triangle you just need to add up all the side lengths so we're going to be adding a plus b plus c all different side lengths that we have here so i'm going to go ahead and add those and say that is going to be 23.7 plus 8 plus 15.

[00:09:53]add up all those numbers and you get the perimeter of the triangle which is 46.7 centimeters if you haven't figured it out by now the perimeter is just the units that is involved in this problem which is the centimeters and the area is the units squared right like square units so let's also go and calculate the area to this triangle so for the area of this triangle i know that it's one half the base times the height now a little bit more about this the height will always be the side that's kind of forming the right angle right there with the base they're always right next to each other with each other all right those two are going to be involved with each other the base and the height so if we go ahead and calculate this we're going to say this is going to be one half times the hot the base is what i had first so i'm going to say 23.7 times the height which is 6. okay now if you want to do this on a calculator of course you can just enter 0.5 as your decimal for one half and you can just go ahead and enter it all in on a calculator and if you do you would figure out the area is 71.1 centimeters squared all right let's move on to example 11.

[00:11:01]we have the area of the triangle is 28 centimeters squared and the height is 4 centimeters find the length of the base they didn't give us a picture for this one but we do know that we right off the bat are talking about area of a triangle so i know area is one-half base height and they also gave us the area of the triangle to be 28 centimeters squared and they gave us the height the other information there so that's equal to one-half times the base times four centimeters okay now when i do these problems i like to take uh the half of the four and kind of deal with the half right off the bat so i'm gonna say this is 28 centimeters squared equals b times two centimeters kind of combining combining these two right off the bat right because i can multiply in any order so i'm gonna combine those two and then it makes a lot easier for me to see that i just need to divide by two on both sides and figure out that b is equal to 28 divided by 2 which is 14. remember we talked about those with those units i'm dividing centimeters squared by centimeters i would just be left with a single centimeters all right number 12 is in your quick check as are the other problems that i have skipped they will be in your quick check for you to try follow the examples that they are next to if you need help let's talk about the circle first of all we have the r is the radius of the circle demonstrated by picture and the d is the diameter of the circle the diameter is twice as long as the radius so if you ever need to find one or the other you can use this the formula right here which says the diameter is equal to two times the radius circumference is the distance around the circle and we talked about that earlier c equals 2 times pi times r again this is really important make sure when you use pi in these problems in your quick checks make sure you're using 3.14 as your pi all right so you're gonna have to type it in i know your calculator may have a pi button but please keep using 3.14 so we are all using the same thing all right let's go through an example here we have example 13 we want to find the length of the diameter if the radius is 4.7 inches so again we have the formula right up there diameter is equal to 2 times r so we can just say diameter equals 2 times r they give us the radius it is 4.7 so we can say diameter is 2 times 4.7 inches into the diameter is equal to 9.4 inches all right a couple more examples here guys just a couple more seconds example 14 we're going to find the length of the radius if the diameter is 83 feet so with this guy right here we again we're talking about the diameter and radius formula so diameter is two times the radius and this time we're doing it backwards they give us the diameter 83 feet and we are trying to find the radius so in this case here we're going to actually divide both sides by two figure out the radius is 83 divided by two which is 41.5 feet all right example 15.

[00:14:03]we'll find the circumference of the circle with a radius of 2.9 feet round to one decimal place so this is where we start involving our 3.14 and we're going to have a lot of decimals but i want to make sure you're rounding it to one when you enter it in your quick checks so for this one we're talking about circumference so we need that circumference formula which is 2 times pi times r and in this problem right here we know that we have the radius is 2.9 so we're going to say the circumference is equal to 2 times 3.14 times the radius which is 2.9 feet i'm going to just type this in my calculator and if you do you should get something along the lines of like 18.212.

[00:14:46]it keeps going feet but we want to make sure we round this to one decimal place correctly so when i round this to one decimal place remember you check the spot after i'm gonna check that one and i know that it it rounds down right so i might call this 18.2 feet all right our last example for today is for the area of a circle with a diameter of 16 meters so diameter is underlined there because if you remember the area of a circle formula area is equal to pi times r squared so we actually need the radius so let's go ahead and quickly go back and find our radius using the fact that diameter is equal to 2 times the radius and we know this is 16 meters is 2 times the radius and so the radius is equal to 8 meters all right so if we go through and calculate this we're going to say the area is equal to 3.14 times that 8 meters squared or again if you don't have that square feature on your calculator you could also of course just do area is pi times r times r and multiply it twice in any case you should be getting an answer of 200.96 29.96 meters squared again read the directions on how we ask you to round but if we ask you to round to one decimal then in this case you would actually round up a lot here because uh we have a nine as our one decimal place but the six you know if we we check that six is round up so that would cause the nine to round up which would cause the next digit to round up so if we round this to one decimal place we'd actually call this 201 meters squared all right that wraps it up for this last notes on 1.7 let us know if you guys have any questions