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Цаг: 0:00Нийт үргэлжлэх хугацаа:7:02

Video transcript

so I have a square here and let's say that its height is 1 meter so this height right over here that is 1 meter now let's say its width is also 1 meter so I'm talking about the dimensions of the entire square not just the shaded region so this is also that right over there is also 1 meter so what's the area of the entire square going to be not just the shaded region the entire square well the total area total area is going to be equal to the height times the width so 1 meter times 1 meter 1 times 1 is of course 1 and meters times meters we could write that as a square meter or meter squared however you want to think about it now with that out of the way now let's focus on the shaded area let's think about what that is so the shaded shaded shaded area is equal to 1 and I encourage you to pause the video and try to figure that out well the one thing that might jump out at you is that our entire area our entire square is divided into these equally equal equal rectangles so one way to think about is well what is the area of each of these equal rectangles for example what is the area of that rectangle right over there and to figure it out we could say well what fraction is that of the whole and to figure that out we have to figure out how many of these rectangles has our whole been divided into so we could we could try to count them out or we could say let's see I have 1 2 3 4 5 6 7 8 9 10 columns and each column has 1 2 3 4 5 6 7 so we have 10 columns of 7 or we have 70 of these rectangles that our entire whole is divided into 7 T equal sections that we see in these rectangles right over here so this character this character right over there that is 170th of the entire area so 170th of 1 square meter which is of course just going to be 170th of a square meter that's just one of these that's just one of these rectangles now if we care about the shaded area we could count how many of these rectangles there are and we see we see that there are 1 2 3 4 5 6 7 8 9 columns of 1 2 3 so there's 27 of these of these rectangles of these equal rectangles in the shaded area so the shaded area is going to be we have 27 of these rectangles and each of them and then each of them have an area of 170th of a square meter 170th of a square meter and what does that give us well that gives us the area of the shaded or the shaded area is going to be 27 70 it's 27 times 1 70th is going to be 27 70 it's 27 70 it's square meters and we're done but what I want to appreciate now is that there's multiple ways that we could have tackled this another way we could have tackled it is to figure out what the dimensions what the dimensions are of the shaded area so for example for example what is what is the height of just the shaded area so just that height right over there and I encourage you to pause the video and try to think about what it is and it's going to be a fraction well we see if we if we're going in the vertical direction we've divided this one meter we've divided it into 1 2 3 4 5 let me do a little bit differently we've divided it into 1 2 3 4 5 6 7 equal sections that might have been a little bit confusing the way I just drew it so you can see it when you look at the actual lecture let me do it in a in a more vibrant color so we have we have I'm having trouble picking colors all right here we go we have one that's that right over there 2 3 4 5 6 7 equal sections that we've divided this 1 meter in and the height of the shaded area is 3 of them so this height right over here this height right over here is 3/7 of the hole and the hole is a meter so it's 3/7 of a meter now by that same logic what is the width going to be what is the width going to be well we can see that the entire meter has been divided into 1 2 3 4 5 6 7 8 9 10 equal sections so going from here to here is going to be 1/10 so this distance right over here is going to be 1/10 let me do that a color that's different so so this distance right over here is going to be 1/10 and so how many tenths represent the width of the green area let's see we get we have 1/10 2/10 3/10 4/10 5/10 6/10 7/10 8/10 9/10 so this width is 9/10 of this whole length which is a meter so it's 9/10 of a meter and now to find the area we can multiply the width times the height or the height times the width so we could say so I'll write this again the shaded area shaded area instead of doing it this way we could say all right I have a height of 3/7 of a meter so 3/7 meters and then I can multiply that times our width for just a shaded area which is 9/10 of a meter 9/10 of a meter and now what is this going to get us well this is going to be equal to the meters times the meters is going to get square meters which is what we want and then we can multiply the numerators and multiply the denominators 3 times 9 is going to give us 27 and 7 times 10 is going to give us 70 exactly what we had before 2770 its square let me write it a little bit neater 27 27 7/8 of a square meter and you could think about why did this work out to put regardless of how we did it notice 3 & 9 in the numerators that was how many rows and columns we had of these little rectangles and then the 7 and 10 that's figure out how many rectangles we actually had so this is say okay the three times nine is how many rectangles we have and then the seven times ten is what fraction of the whole each of those rectangles represent and that's essentially what we did up here so either way you're going to get the right answer but I really want you to think about why this was