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Math 7 - Module 1D - Lesson 19

Added Jan 15, 2021 •

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What is the Area Factor, AF? How does the Scale Factor, SF relate to the Area Factor? Given the Area Factor, find the Scale Factor. Given the Scale Factor, find the Area Factor. Use the Area Factor to find the Area of a Polygon if given the Area of another proportional Polygon. Old Measurement X Scale Factor = New Measurement Old Area X Area Factor = New Area

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so lesson 19 Computing actual areas from a scale drawing finding the areas based on a scale drawing we're going to go to that just a little bit by little bit we're going to butt area is there to area is there we're going to have more eventually but let's do a quick review if you remember I want people to put it in the chat do what hair looks do this looks right at down area so area formula we're doing Tuesday Pacific areas we're going to work on today area of a rectangle and a square are pretty much the same thing area I'm a rectangle anybody know type it in the chat don't say it out cuz I want people to Chance the give people a chance to think we all first went over at take fourth grade they would deliver more bass work at this rate and last year in 6th grade you put it in word problems used it all right I'll take that I'll take that says that right there's a good description what was the formula okay what do you do with yes totally correct on that one but is there a another set of words for those two parts so I'll get both of them though so yes yes yes totally correct all you guys are correct so you lot of people says * * your correct we do some people didn't say what though some people just said the sides of any two sides in a rectangle length conduit to multiply length x wicks that is the formula to find the area of a rectangle that's pretty much I don't know of a better word but it bites that don't don't take offense to it this is the Elementary Middle School definition but you're halfway through middle school so starting from here on out most teachers in math after this won't use 8 * what do use this instead base times height the base is either the bottom or the top side one or the other not both that same time if we're talking both of the same time their base says it should be the same in a rectangle and height is how tall something is so you look how flat something is parallel to the ground and then you looking house something is so base times height now wishes that does anyone know the area of a triangle anybody know the formula for the area of a triangle Summoners War last year some guys did that's okay I just want to see who knows I got some faces it's three sides yes but how do you find the area so here's we're going to go through area really quickly get to hear but how do you find it a very similar so here it is there's two ways of writing it I use the second one but Imma do it the first one first it's 1/2 base times height running out of space on a short-handed were you multiply your base times height and then you divide by 2 base times height divided by 2 that's the same thing another way of that is another way of writing this 1/2 base times height here 1/2 the same thing as DH over to base times height divided by 2 that's just like a rectangle but half of rectangle so a lot of people are always wondering how is it has the rectangle so you got to think like this right here here's your the bases are the bottom or the top but let's go with the bottom cuz you know we visualized based on the bottom of the base of a cup the base of a the base of your of plants So based and height is how tall it is and here you got to think right now let's look at this that's base times height tangle again cut it in half cuz the area of a triangle is half of rectangle if you look at it but most people cut a rectangle and half yes you can leave your screen on so going straight down this way or straight across this way but most people don't think you can actually cut a rectangle in half also this way this top triangle is the same as this bottom triangle so the area of a triangle is half the value of a rectangle that's where that formula comes from all right now that we know got a quick lesson on how to find the area of a rectangle and triangle we're going to use the coming up so let's go right here how to find the area from a scale drawing well actually we don't need to but we're just using this we're going to see how things relay so let's go with this right here what is the scale factor the scale factor so we're going right here will look when we're going to look for the scale factor we're going to look for the actual here actual area we're going to look for the scale drawing area and then after that we're going to find the value of ratio value of the ratio when making a fraction value of the ratio and look at this ratio of what the scale drawing to the actual area so it's scale drawing over the area actual area so some people said didn't I say it's supposed to be real life on top it should be but it's not all what makes it hard for a lot of people to fight with the scale factor is is what number goes on top what number goes on bottom totally understand that that's why I Lexile your reading Lexile or just looks out. Understanding is showing this last one to do this first one it would have been nice if you read all the way to the bottom cuz this tells you how to set it up scale drawing to the actual drawing scale drawing to the acronym this over this and a way to remember scale factor scale factor the better thing to understand scale factor scale remember let's be lazy anytime you want to write scale factor go SF keep it short and sweet should be should be the new over the old but some people get confused what's the new one what's the old one there's another way of saying it and some people remembered this which is actually good it's what you want over what exist once I want the scale drawing to the actual area so that tells you how to set it up and remember your a factor is jest just what is just k your constant of proportionality SF another way of saying that is that variable k k your constant of proportionality proportion what was K again if you remember k that is why I over ex y over x equals K which is the concept of Personality which is the scale factor SF over old what you want over wet exist to go over and then look at all this yet someone said look at all this and we got a drawing and we got to fill this in organize yourself number in that first lesson about the stuff we said organizers up with a t chart that helps so when you make a t chart again we'll see you guys just like this which one goes to the left which one goes to the right remember why an ex this one is your ex decide is your why so if it's y over X Y over X Y over X new is my wife so this side has to be the new beside has to be the old and so we're going from old to new but when we find a scale factor it's new to old looking at this I know a lot a lot so far just explaining all these little bits but two and three would be really fast we're going to take time on number one to make sure you understand everything going back let's do a review put this in the chat looking at this start here in this picture and then we go to hear the second picture what type of scale do we have what are we doing there's two choices you're going from here to here what is it what is this what type of skin is it what type yeah that's a good technical term going from this to this what is it looking at it remember our first lesson Lesson 16 I believe it was yes you are correct what are we doing we're going from this smaller one to this bigger one hint in the small one to this bigger one what are we what is this called it's a what two people good good type it in let me see yes you are correct for those that answer it is an enlargement this little bit of information will help you cuz remember if it is an enlargement your scale factor has to be bigger than one if you have a fraction less than one to give you a clue that you messed up this is mass stinking how to check your work we're going from small to big that means the number or scale factor has to be bigger than one so it's less than one you got things switched around that helps you check your answer so old vs new so let's put our measurement here's our old one we got four and then we go to four let's match up our base to our base what's our new 1/8 what's look at our old height our old height is let's go 3 and our new height is 6 326 so what is our scale factor so you want to set it up look at this new over the old so let's go with this 1/8 / 4 or do we do 6 / 3 new / old but if you look at both of them they're technically yes if you look at both of them they are technically the same as 8 / 46 / 3 both of these are equal to and I'll write it as a fraction first 2/1 which is the same thing as too our scale factor is to what does that mean no scaling if it's bigger than one it means a enlarged is this many times it is so compared yeah yes so from this one too first one we doubled it this is double the size of this one we blew it up two times we enlarge it just imagine I use this example here is Bruce Banner this Incredible Hulk the Hulk grows bigger it's just a bigger version accept metal monster purse a green monster retina so they largement Bruce Banner doubles the size when he comes out but I think the whole game if you read Marvel handbook I think the host is like that 3 in 3 and 1/2 to 4 and 1/2 x depend on which Hulk so Bruce Banner blow up twice as big but let's look at the area now so let's go here let's look at the area the area for this one is okay for dates different colors of the 48 area the area of the first one the base the bottom the floor is for how tall is it from there three the arrow what is 4 * 3 which is 12 that's pretty easy pretty easy the second area let's write this down so that's the actual pictures or actual area is 12 Melissa guitar scale drawing area the area for this one the base is 8 the fight is 6 8 * 6 so it's 48 so the scale factor so this is something we're going to look into that I'm giving you a hint the scale all the sides are doubled look at that Ford all the McCain 83 double DIN became 6 but you look at the area though the area of the first one is 12 but the area of the second one is 48 that's not double that's not double keep that in mind though we'll get to that in a second or not a second look at more let's read this let's write the rate of value of the ratio write the fraction of the scale drawing area to the actuator children area 48 the actual are natural area is 12 48 / 12 simplify this fraction simplify this fraction somewhere. Just someone what is 48 over 12 simple simplify to I'm going to give a second type it in the chat type in the chat this lets me know do you know what for 8/12 simplifies to you are correct this right here was lessons one two and three some people had issues with this cuz they didn't understand pretty much oppression you are correct you are correct which simplifies to what so one more step one more step what is that become yes correct so I'm going to do extra bit of work you are correct yes 248 / 12 is another way of writing or reading 48 / 12 but if you look at it as a fraction which confused so people you got to learn to understand fractions or another way of writing Division if you understand that simplify this 48 + 12 what do they share when I say share what can I divide top and bottom eyelashes / 12 that's the biggest some of you guys didn't finish it some of you guys divided by 4 and then you ended with 12/3 but 12/3 with 12 / 3 keep on doing it till simplify 12 / 12 that's a 148 / 12 that's for 4/1 4 so the ratios a scale factor is the race of comparing sides if I compare the sides it's double but if I compare the area it's quadrupled hint intense double what's the weather next one using so you're going to do this right here I'm going to do now I'm going to give you a minute and a half using this setup right here you do these right here you just saw how to do it simple someone said it's super easy I can do it yes I know you could do it so finish it I'm going to give you one minute 30 seconds do the singer on stop looking away stop looking at your other screen stop watching your video fill this out do all this stuff your turn don't wait for me do this so he can see that you can do this work you can I know you can write don't do this on your own find the scale factor actual area scale drawing area and the ratio of scale drawing area area to the actual area do this right here and when you are done I've done if you're stuck type stuck so I know I can move on don't take down until you're done what is the status status all right it lets me know at least you got somewhere all right that's more than a minute and a half so you should be done check your answers if you're copying me right now come on this was easy all you had to say I don't get it what that was that's one of them all right let's get so first let's set up our scale factor but let's look at it we're going from here here so looking at it now I got this Incredible Hulk is huge but now it becomes puny. Yeah yes some you guys that are smiling see that means you at least you're watching the whole cart and then you know I'm talking about remember the Hulk always cause Banner UNG Banner my fault you don't you know you don't you're not answer the Marvel stick with DC go watch your flash cartoon TV show so this right here Hulk shrinks down to become batter so let's do that the whole tricks done to become better so it's up reduction by knowing this this is just this is not this is more science observation the first rule in science when you're doing a science project I think is the Absurd will hypothesis the first thing but the observation is the next thing we're observing that big Hulk becomes puny Banner so logic science and math thinking tells us that the scale factor is going to be less than one it means it's shrinking it's this this is the original size what happens so it can't be one whole it needs to be a fraction of this this is a fraction of that so that helps us get the scale factor so that's where people get stuck number goes on top and bottom that's why you need to know and largement versus reduction bigger than one Westin one but how do we set it up if you're lost and stuck that's why you always want to stay organized T chart let's make a t chart old and new and since a lot of guys don't want to have colored markers and pens I'll just use black old new some Eagles. Blue stupid blue or one color let's zoom in now alright so here's the old number I hear the old the end-all here is the math part you need to match the corresponding size matching sides not just any song the bottom of this rectangle needs to match up with the bottom of this rectangle bottom to bottom 622 Base to Base the height of the original the old angle is 9 the height of little rectangle is 3923 this is a little bit of extra work that I'm doing I'm putting down both of these numbers only because I want to show you both of them this up here tells you that both of these this is a scale drawing which means you only need to compare one set I got two sets I don't need to do both of them, do it down here instead of writing it feel like that down here new versus old so I only need to choose one of these sets cuz I know they're both going to be the same because there's actual picture and it literally says scale drawing over old 2/6 simplify this fraction I could / 2 / 2 and my equivalent how do you make equal fractions by multiplying or dividing by the same top and bottom / 2 / 2 2 / 21623 that is my scale factor 1/3 hey reduction less than 1 look at the next one I'm going this one just for the heck of it and give me the same thing 3/9 Miu over old 3/9 but notice this one this one I / to this one I'm too into but this one divided by 3/3 it's a different number but it still gets me to the same answer 3 divided by 319 divided by 331 third boom did I have both of them know can you do both of them yes but do you have to know that's the difference between a c student compared to a b and an a student a c student just does the works cuz they're following the recipe in back of the box go back to the brownie mix you can still make a pretty tasty brownie the box but the Beast doing realizes they said use oil why don't I use butter instead it's going to be better tasting cuz butter is technically a form of oil do you put butter instead so yet kind of change it up the same I don't need to do all of it but I could do this in a soon as like a man I can make super fancy now I got my brownies in there I don't just have to put brownies I could put chocolate chips in there I can make chocolate chip brownies cuz you know that it's not going to make it any worse you're just going to make it better and same thing the A and B Street and realized I don't need to do both of them one of them works I just need one of them if you do both of them that's fine not maturing at the wrong answer just you're doing more work than you need all right so that is our scale factor talk too much right there what's the current area the area of the Hulk figure so the area is base times height the base is 6 the height is 9 6 * 9 that is 54 so the area of the actual picture is 54 MLS go with this right here the area is the base is to the base the base floor the height is 3 which is 2 * 3 is 6 so the area of that is 6 now we got these two numbers all we have to do right here scale drawing of the area to the actual area scale drawing Area Pediatrics 6 over 54 and we simplified 6/54 simplifies to 6 / 61504 / 6 9 notice the scale factor the size I / 3A / 3A shrank both of these to this by dividing both of these by 3 / 3x down that much together that's ask area Factor that's 1/9 what does that mean so let's look at this so I'm going to do a quick review on what area lol you guys gave me this you told me you remember that you knew the formula to how to find the area what does area mean here's what people get mixed up with why do you guys some people and I acknowledge you now I didn't ignore you someone said right here isn't the area 14 not 12 here's how the person got 14 4 + 3 + 4 + 3 that is called the perimeter when you go around a shape when you find the length around the shape that's called the perimeter that's like you know you walk the track you run the track you run the perimeter of the track you will you know if you put a fence around your house the perimeter of your house so a perimeter is all the links around added together area area your play area is the space in between an area is always measured in square units that's why we look at inside each of these they're not inside each of these are squares we measure everything in square units some of you guys have told me you moved into a new place or you help a route that's why the other day some of the three of you in 10 test was that a coincidence help family member move to a new place or some of you guys went to go with your aunt or Uncle to look at a new apartment or condo house whatever but one of the things you need to understand when you go to a place people sent start smaller blah blah blah but if you look at the piece of paper they always give you the first thing that was tati is the square footage of the place the square footage of the bedroom the square footage of the whole property square feet so you measure play I'm in the garage right now I don't know what the size is but I would measure the garage little squares 1 foot by 1 foot square unit so we count those numbers to look at this the area of this rectangle is 12 that means there's twelve little squares in here 4 across with 3 Rows 4 * 312 squares total this right here I got eight squares across six squares up how many total square little square 48 square units area right here I got six across and 9 Rose 6 X 9 that's 54 little squares in here and you can easily see two units across three up to 4 6 little squares that's what area means if you look at this 54 to 6 that's not going down three times that's going down 9 times look at this up here the size switching is double but the area didn't go down then go up by 2 it went up by 4 that's a hint right there think about that next one use this formula right here area of a triangle is base times height divided by 2 you're doing the same thing 1 minute 30 seconds fill this one out right here just this don't go below will do the spark together up here pencil or pen or crayon to paper and do these tell me the scale factor of the triangles the are actual area of this triangle the actual area of this triangle ratio this one over this one area over area finish do this don't be shaking your head get a pencil stop complaining there are a couple of you that are no longer on the screen or your screen is off I'm about to remove you you should always be in the camera you should not be watching SharkBoy and Lavagirl right now I'm trying to watch right now cuz they put up the sequel that that everyone can be heroes I have to watch that so I don't remember Sharkboy and Lavagirl I'm not going to watch this movie and tell her why finish watching SharkBoy and Lavagirl I have to watch it anyways cuz everyone watched it while I talk about how bad the acting of boy was he hasn't done anything since Twilight now he did a couple movies no no so that movie everyone can be heroes is actually a sequel to Sharkboy and Lavagirl I know hey I watch Sharkboy and I remember watching it when I was younger only because it was in 3D sounds like one of the first 3D movies to come back get your camera on I'm about to remove you I gave you the morning 3 second turn camera on ICC I'm also one of those people that like to read the books before I watch a movie to see how it's a complain about how bad the movie is I knew Twilight was going to be a bad movie but I read the book to I read all four of them I'm angry that I read those books I started it but I had to finish it and I'm angry that I had to watch those movies to the last one is actually pretty good actions and there's a good fight scene at the end but it turned out to be a lie I'll say this I actually thought about the final fight in the last Twilight movie was better than the Avengers endgame is The Avengers go watch it again that you play zoom in on all these characters but all in the background you can't really see anything as having it was so messy you know besides when when when when Spider-Man gave the gauntlet to 2 Sea Captain Marvel and then the black guy that was the only good sequence at the end for the last fight the rest of it was messy messy messy cuz everyone's done thank you for trying all right let's put the formula down so we don't mess it up cuz it's a triangle and a rectangle the area of triangle is base times height I'll put the time that's not beat d x h b t h over to base times height divided by 2 level for this let's go do our T chart Old versus the new so are all base the base has the floor is 6 the new base is 8 let's compare that to help out all these triangles are you are pretty much dead that's right how tall is it its 9 how tall is this 12 take one of these any one of these because we know it's a scale drawing it doesn't matter which I'm asking to do both but you only knew one of them I'm going to go 8/6 just to show you so 8/6 I can do by both of these by 2 / 2 I get 4 / 2 I get three my scale factor is 4/3 and now I'm going to do the other one just to prove to you it's the same thing let's go 12 / 9 12 + 9 I could divide 3 on both of them what's 12 / 349 / 3 34 3rd stairs my scale factor boom now let's look at our area though good I had it right but let's go base times height here's my base 6 times my height which is 9 but then you have to divide it by 2 so that is 54 / 2 what you are totally correct equals 27 NOLA city of the month same thing same process good job check your answers the reason for you to check your answers is to say hey can you do this right now is the perfect time to make your mistakes cuz you can learn how to fix it if you're going to wait till the test to do any of this stuff too late I can't help you but right now I can so area our base is 8 our height is 12 and then whatever we get we / 2 8 * 12 is 90 + 96 and over to half of 96 is 48 the 4848 so horny 8 and we want our Ratio or scale drawing of scale drawing over the actual so 48 over 27 what does that simplify to this right here by / just start going through listing both of these even / to commit / 3 yes 27 / 3 is 914 / 3 is 16 there's your answer hey look there's my scale factor and look at my actual area factor and I did mention that scale factor I'm comparing my side to my side but this right here I'm comparing my area to my area so this right here there's another name for this it's called the area that or since we're too lazy when I'm too lazy imma let you know where your area factor is AF area Factor that's a special number so let's collect let's fill in these two to get fill in these together and see if you see something because it's written like this what information this is just like science we did three experiments we did three experiments some of the stuff is kind of messed up it's a lot of information in detail what do you do in a science experiment at the end you take what's important and squeeze it down just like an s say in English we're going to condense all the stuff to what's probably important what's the best zoom in here look at your old notes look at both of the pages look at both the babies cuz we're going to fill in these lines what do you notice about the ratios of the areas and examples 1 2 and 3 complete the statements below when the scale factor was too so that's on the first one what was the value of the ratio of areas so the scale factor was to what was the last time the scale factor was to the area Factor was for now look at this you can leave the camera on though to be came for now listen to this on the second one the scale factor was 1/3 scale factor was 1/3 and then we're looking for the ratio of areas one and we just did this last one up here I was just going to bring it down right here the scale factor was 4/3 and then the ratio of areas was 16 / 9 this leads into the next one what can we conclude but let's look at this right here I want to take a minute or two for you to think about it and look so this side right here all three of these numbers these are the scale factors all three of these numbers are the area Factor so we'd line them up so you can see them side-by-side scale factor the area Factor scale factor to area Mario Factor 2 Sims 4 1/3 becomes one night I want Birds becomes 16/9 does anybody see a pad how's this becomes this how this becomes this what is a you so that would be called a mass rule what is a same thing that all of them do to become the other number how to become four how does 1/3 become what a night how does 4/3 become 16 dimes what's same thing that we do all of them I want you to think of it okay that's the operation but what do we operate how do you go from one to the other I'm going to write it down to the second but I do like what you're thinking so look at this so how does two so I got two people that's what we be times that we multiplied it you're actually correct but that's not the whole thing I want so think about it let me write this down though I'm going to use three Tyler so we could differentiate all right let's go with all right too became for so how does too I'm going to give it to us to end up equal for how does 1/3 + 1/3 equal in one nights how does 4/3 and 1/5 equal 16 and for all of these this right here is science in terms of what it means logic logic is science and math thinking that I would try to get you guys to do on the stem stuff I'm going to go back to someone said two people said we * 2 * what 1/3 times what 4/3 times 2 * what for 1/3 * 1 text me one nice 4/3 times what gets me 16 lights what did we just do I get what you're saying you're actually so close to saying the right answer so close I'm going to wait what do we do what do we X and this right here is just like a puzzle this is what makes math mask using your logic to figure out something this right here will leave some of you guys to computer programming like I said you can make an app if you make app that lot of people buy you could come on the next Zoom screen if you make it in a week and say Liang and then you throw all this bad stuff you say bad things about me look at me look at me I'm a millionaire now but are you you nothing you're below me but that's nothing you had to use logic I would love for you guys to do that make me proud to say it like that that person 2 times what gets me for 2 all right but 1/3 * 2 that's not 1/9 1/3 times what number gets me 1/9 it's another fraction look at this one third times one third one times 113 times 394 thirds times what gets me good see the pattern 4/3 * 4/3 equals 16/9 here it is what is this tool to represent the scale factor 1/3 represents a scale factor 4/3 represents a scale factor the scale factor times the scale factor equals what are all these numbers these are the ratios of the areas that's the area that and someone just wrote down good observation can't you write this scale factor time scale factor yes I'm going to write it down for you another way to write scale factor time scale factor summer guys know it scale factor squared new square number for those that don't know what an exponent is the exponent says this is how many times I'm going to multiply the same number by like here 2 squared it's two times to that equals for this next one is 1/3 Square that's one third times one third one nights 4/3 squared this is just a shortcut of writing repeated multiplication what does 4/3 x 4/3 listen to how I listen to how much I used to have to say 4/3 * 4/3 Portland Square let's talkin shortcut for 30 * 4/3 + 16/9 so that right there both of these are the same thing how do you find the area Factor if you find the scale factor just Square we don't need to define the area waste of time is the scale factor of the size is are in the ratio of the areas is r squared or r x r it's up to you which one's better slip to pay just go on the next one will do this one together this right here is leftover is it a continuation of bass lesson lesson 18 19 lesson 18 we had that story about the the student wanting to build a basketball court and are they wanted to build a basketball court almost almost done we just got finish this and couple more neutralize so this is a continuation of that problem so if you got your lesson 18 notes with you that will help but I'm going to go over the major parts the main parts so you don't need to do the student government like your half court basketball plan they have asked you to calculate the actual area of the court so they can estimate the cost of Project based on your drawing below what will the area of the plan half-court be so I will bring in the information from last time so we're going to do this new method 90% of the Spanish dancer and then I'm going to bring in the information from the old picture so I can figure it out so let's look at our first no matter what we need to find our scale factor members scale factor come from scale drawing scale drawing is 1 in on the drawing corresponds to 15 ft in actual length scale factor equals what we want over what exist new versus old this is our old one we want to actually build a real new basketball court we watch the basketball court so that's why I wrote wants verse exit instead of new over old we want real life so real life is 15 what we have in our picture right now the old is 1 inch so the scale factor is 15 so I'm going to rain so scale factor equals 15 that step one but I want to find the area so I'm going to put this down from last time so we can match it up remember what if we're looking for if we have a drawing and we want to find the new measurements and we also have the scale factor remember there was an equation we had the old measurement old and I'll put the word length lynx measurement and we multiply that by the scale factor that got us the new length measurement but we're not looking for length now we're looking for right here where do they have asked you to calculate the actual area so we want area so let's look at this instead of length measurement let's go with old area old area here's where people the mistake we're not using a scale factor factor so you know the area but instead of scale factor x the area factor to find the new area all right that's nuts but tend to be the stuff you keeping your head like mental stuff right here was plugging in the old area which means is the mini area so base times height with our base is to times are height is 1 and 2/3 I'm doing one extra step before I write it down we don't like mixed numbers to change into an improper fraction that was you guys they need fraction help pay attention right here is a mixed number 1 and 2/3 you take your denominator so you're you take your denominator X your whole number three times once that's three and you add it to your numerator 2 3 x + 2 5 so are fraction is 5/3 time the area Factor up here we have the scale factor so that means we need to find the area Factor area factor which we just learn from the last page is just the scale factor x the scale factor I'm writing this way instead of scale factor Square because a lot of guys aren't good with the exponents yet I'd rather you start with this right now so if you good with exponents go ahead area Factor equals put in what's the scale factor r scale factor is hey * 15 for those that are paying attention I need to know so so I could give you a participation grade on Friday yeah participation rate end of the week that's another thing I forgot that I'm telling you I'm doing what's 15 * 15 * 15 * 15 come on you should know this what's 15 * 15 let me know you're paying attention you are correct you are correct you are correct your correct you are wrong you're correct correct correct correct when I said you were wrong and you typed in the wrong number one wrong number check your work but I should be right yes everyone is correct 15 * 15 225 so you take this * 225 you get your new area notice I'm not even looking for my new sides so this is only thing we got to worry about if I'm multiplying fractions I got to put it over 1/2 * 5 is 10 * 3 is 310 thirds * 225 over 1 that is * 10 2250 / 3 notice what I said 2250 divided by 3 I can't do that in my head some dude off to the side 32253 goes in a 20 to 7 times cuz the closest numbers 20141 I subtract get a one bring down the five how many threes are in 15 V 50 - 15 + 0 I bring down this zero how many threes are in 00 750 750 square feet so the basketball court is 750 sq ft you know what 750 square feet is a big room the bedroom big bed big bedroom or a small Fondo it's like the Bungalows if we went back to class each class would be about 700 bigger so here this is using the formula I didn't have any measurements of you guys looked it up thank you for looking it up I acknowledge you why do you guys remember so if one inch is 15 ft remember to in is 30 feet and Latias wrote down you remember that was 25 feet how do you find the area of anything length times width 4 base times height in this case it is 30 * 25 which is just 750 square feet I'm going to stop you before you type it out how come we did is it in the first place we would have had that's a whole thing yesterday we had all that's holding we should have if you saw excuse me if you saw the work that we and remember the work we did yesterday to find these man that's a lot of work just to find measurements so this is actually less work if we hadn't found these first listen to the next one we're going to do this first one together let's read this actually does the actual area you found reflect the results we found in examples 1 2 and 3 explain how you know so let's go do this so we can first we go with the area the first area area area 2 and we had scale factor was the scale factor the first the scale factor the area the area and did we did a ratio of area what was it the second one we put up now I'm saying is what we do here like right here doesn't match up Sault area 2 / Area 1 which is also called the area factor is that the same thing so the scale factor the scale factor was what the scale factor was 15 of fire we got that scale factor was 15 the first little area that area of our little diagram was 10 / 3 the second area we just found that out with 750 does this get us our area that does this when we get our area Factor so remember 15 squared scale factor squared is 15 squared that is equal to 220 let's check to see if our area Factor setting it up this way that's it so 750 / 10/3 if that doesn't look fun to do complex fraction remember when we have a complex fraction a fraction inside of a fraction do not write it as a fraction don't look at as a fraction rewrite it as a division problem 750 / 10/3 and when you write it as dividing fractions you need to remember to change the division into multiplication to make it easier 750 * 3/10 division becomes multiplying the reciprocal and this becomes 2250 / which we have placeholder zeros 225 the area Factor equals 225 and up here scale factor 15 squared equals to 25 which equals the area factor which one is better to do this one Define the area Factor the constant of the area's the poor my area set up the square the scale factor instead of just setting up my look at all this work look at all of this work to get the area Factor when we could have just done all right if you like this way go ahead all right so what's that this up together we got just enough time let me see yes we got 10 minutes we could do this first part together and for those guys that are going to show up in a bit to academics cuz the exercise you're trying these parts on your own but we'll work on this first part together try these other parts on your own and if you feel comfortable you're ready to go for the problem set but if you don't feel comfortable where we can work through this together in academic support coming up set after this right here right here this is considered a little bit harder more difficult question only because I haven't said it yet and I'll tell you why the triangle depicted right here depicts the dwell the triangle depicted by the drawing and actual area of 36 square units what is this scale of the drawing what so they're singing real life does this real life drawing that we have cuz it's the actual are is 36 square units has 36 squares in it but this here is what we have what makes this one harder is cuz we don't have a pic the other triangle notice all these other things or this one doesn't either but notice all of these right here we got to drawings the matchup this what you can always do is write draw a sketch so you can visualize it information says we got another triangle we have another triangle and we know the area equals 36 and then we have this one right here what is the scale of the drawing that means we're going from Big this one right here to this one yes we can do that too yes we will let's finish these first so you go from here to here while we got to find what this is and notice right here here's a hint no each Square on the grid has a length of 1 unit was so how long is this little triangle 1 2 3 4 5 6 so that means that's 6 units long what is the height of the triangle 123 that means it's three long what is the area of this triangle Sault area equals the base times height divided by 2 18 / 2 the area is 9 look at this right here so we're going from here to you here's our original if usually wants the scale of what we want over what exists so let's find the air so we got area we can find the area Factor so the area Factor so the area Factor so these are the two areas the area Factor remember is what we want over what or what's the new verse of the old again they both work but in this case what do we want we want the scale drawing what is the scale drawing what is a scale of the drawing is a scale drawing so we want is this number over this number and the two numbers that match up are the areas so 9 over 36 and I'm acknowledge you in a second we can simplify this and this part beat okay three people. Thank you 9/36 is equal to a simplified version of 1/4 and that's the area factor I messed up I should have put area fact or not area what's the area Factor it's so right here it wants the scale so this problem is how do you take the area factor and bring it back down to the scale factor so you can find the scale okay I got that that's fine this right here it's simple but it's the hardest things for love you in math to do write down the formula write down something you know we're trying to find the scale factor so this is the answer then scale factor equals? We're trying to find out the scale factor equals what we have is the area Factor how does the area Factor connect scale factor this right here the air you know the area factor is equal to the scale factor x the scale factor once we find what one of these are we can just write what that is we don't have that what we what is this right here the area factor which is 1/4 1/4 equals the scale factor x the scale factor this is logic right here what same number multiplied by the same number gets you 1/4 when it's a fraction people freak out you got to think this should be a fraction in this should be a fraction what same number times what same number gets you a one and let me ride it while you tell me right there in the chat box what so we know we got for multiplying two fractions what times what gets me one correct 1 * 1 equals 1 where's the next part right when you finish this your answer appears cuz we're just looking for what the scale factor is what's the score the drawing look at this right here 1 x 1 x 1 get this me the one what number times what number gets me to that's the same what times what gets me or yes who what is 1/2 * 1/2 equals 1/4 so our scale factor is just one of these so our scale factor is 1/2 one half so that means our original shrunk down to this so look at this right here that means this if this is one half of this is double so I can 33633 that's nine what's double 612 listen to the area then area equals base times height divided by 2 that should be 36 no double I messed up I 33338 not 93326 I was like what 612 * 612 * 6 is 72 what's half of 72 36 checking my answer so my scale factor is 1/2 this was hard because backwards

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Math 7 - Module 1D - Lesson 19

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