16.3 Problem Solving-Area of Rectangles
Geometry
Let's look at unlocking the problem by solving the area of rectangles
Good morning. We're on 16.3. I'm sure you have your name at the top. Now, let's look at unlock the problem. You need to understand that multiplying the length times the width of a rectangle is the same as multiplying the number in each row, times the number of rows in an array. You can either use either way to find the area. So when you're looking at this first example right here, this times this length times width, the same thing is row towns a number of rows. So it's the same thing as multiplying this way times this way. So you're doing basically the same thing as length times width, it's just different terminology. So let's look at this question. So our essential question for the day is, how can you use a strategy to find a pattern to solve the area problems? So how can you, how can you use the strategy, find a pattern to solve area problems? Well, let's read our first problem. The rectangle show mister coy's plans for storage sheds. How are the areas of the sheds related? How will the shit areas of sheds a and B change? How will the areas of C and D change? Use a graphic organizer to help you solve the problem. Well, the first thing let's kind of look at a and B here.
So we're looking at these two right here. How much bigger does she look than should be? Are some sort of should be then should a well, this is four, then this is 8. So how much bigger do you think it is? It's twice as big. What about C and D? Same thing. Now. So we have three foot and 6 foot. Three foot. And 6 foot. So now only. Is a is a process tall. C, B is twice as tall as D. Now. Understanding all that, let's figure out what we need to find. Well. We have three questions here. First one, how are the areas of the schedule related? The second one is how will the areas of sheds a and B change? The third one is how will the areas of C and D change? So we have three questions to answer. Let's look at what do I need to know. I need to find out how the areas will change from a to B and. Yes. C two D, okay? Now what information am I given? Well, we're given the length. And width, W, D, T, H, of each shed to find its area. So we're given how long it is and how wide it is. What strategy is my, what is my plan or strategy? I will record the areas in a table and I will look for a pattern to see how the areas. Will change.
Now, let's look. I will complete the table to find a fine patterns to solve the problems. Well, look at shed a. Length is three foot. But what is the width? It is four foot. FT is the abbreviation. For foot. Well, what about V, what is the width? Well, it's 8 foot. Now let's find the area. Three times four is. 12. Feet. And three times 8 is. 20 four. Feet. Now let's look at C and D now the length. Of C gives us the width is four, so the length is 6. And D, the width is 8, and the length is 6. So 6 times four is. I forget to do. Got the label my units. Now, 6 times four is. 24 square feet. Zeb abbreviation. Sq period FT. Well, 6 times 8 is 48. Square feet. Now, the area has changed from square feet, 12 ft². To 24 ft². And from 24, square feet. Two. 48. Square feet. I'll see the links will be the same, and the width will be doubled. So when the links are the same in the width are doubled, the areas will what? Well, from 12 to 24 is what? Double. From 24 to 48 is what? Double. We're going to. Double. So when we're looking at this. We're doubling. The linear width. So from three foot four to 8 foot 6 or 6 foot 8, we double.
Four down. No. So let me explain. Share a is three foot four. Three foot by four foot. Shed B. Is three foot, by 8 foot. Now if you look, we go from 12 to 24. Just budget doubling when we double the width or double in the area. Now, look, it should see. From a 6 foot 6 foot 8, 6 foot length of four foot width is 24. But when we keep the same length of 6 foot and we double the width to 8 foot, our total square feet change from 24 to 48. Now, if you'll notice in a and B, we took the width from four to 8. And she had seen shedding, we took the length, just kept the length the same again, and our width was from four to 8. So all we're doing is doubling the width of how wide this is. And we're doubling the amount of area. Think of it this way. You have a desk in front of you. The desk by itself is a certain square feet. If you put two desks together, you've doubled your area. You put four desks to area, I mean, four deaths together, then you quadruple your area. So this is the same concept. Three foot by four foot, if that was what you had in front of you, and you took the same thing, you added another. Four foot to it, it's the same width, but the length is different. It's longer. You're doubling, so you're adding two sets of cubes there. Okay.
Once you're done with this, and you understand have a basic understanding, we can turn the next page. Okay, so we're going to try another problem. Mister coy is planning more storage shits. He wants to know how the area of the sheds are related. How will this areas of sheds even F change? How will the areas of sheds G and H change? Use the graphic organizer to just help you solve the problem. Well, all I need to find. We just need to read the question. Need. To find out the. Area. Will? Change. From C to F and G two H now. What information am I giving? Given. The length. And. Width of each shed. Two, 5, it's. There we go. So what information am I giving? I'm giving the length and the width of each shed to find its area. Strategy. This is before. We're going to record the areas in a table. I'm going to record. The. Areas. And a table. And then look. At that K again, because on a very good-looking K look for a pattern. You have to solve. Well, she had E, or length, is 5 foot. Our width is 8 foot. Should F are length is 5 foot. Now with four foot. Well, 5 times 8. It's 40, square, feet. 5 times four. 20. Square feet. Okay, let's look at G, our link. Ten foot. Ten foot. We're both ten foot. Our width. Said, gee, this is 8 foot. Shared H is four foot. Well, 8 times ten times 8. That's 80. Square foot. Ten times four. That's 40. Square foot. Little wings will be the same in the width. We'll be half.
The areas will change from 40 ft² to Tony square foot, and from 80 ft² to 40 ft². I'm sorry, from 80 to 40. 40 to 20. So when the lengths are the same and the widths are have, the areas where we have. So. What stayed the same, my length? Played the same. And my width were cut in half, so my area is cut in half. Once you have this written down, you can go to the next page. Okay, so how did your table help you find the pattern? So the table helped me see the multiplication needed to find the area. And then. Was able. To. See how they changed. Okay. So what if both the width of the so what so? Sorry. What if both the links and widths of the sheds are doubled? How would the areas change? The area. Would. Be doubled. It was. Or four times. Greater. So for understand this, when you multiply, when you double, this is the easiest way to say this when you double the width, the whole area is going to double. If you double the width and the length of something, then you double it twice. So you're taking it times four. Okay, when you get this written down, you can turn them to the next page. Okay, so we're on the sharing show. We're going to use the table for one through two. Read the question.
So what is our question? How do these areas of the pools and the table change when the blinks? Change, right? Not the way it's the links. So we're looking at this right here. Have you noticed our wit? Those are all the same. So. That's our first question. What stays the same? Let's take this thing. The links. Increase. Let's look. From 20 to 30, what I increased by. We're measuring again. Feet. The areas increase. The square feet. But if you were to wait in two is one 60. 8 times three is two 40. 8 times four is 320. So you can spot these. 400. And if we took 400 minus three 20, zero, ten, ten minus two is 8, goes cross out. That's how you find the difference. What the increase is. So what if the width of each pool was four feet? What would happen? The area. Wood. B. So instead of multiplying everything times four times 8 hundred times four or four and two is four times 20 equals. Anything round. 80 is one 60 right. And since this number is taken the same on the way through, then we'll be half all the way through. Once you get this written down, you can go to the next page.
Okay, look at number three, Elizabeth built a sandlot that is four feet long. And four feet wide, tell us a bit of fire garden. There's four feet long and 60 watts. She built a vegetable garden. It was four feet long and 8 feet wide. We need to run the line and explain how our areas change. What information are we given? Four feet long and four feet wide. Four feet long 6 feet wide. Four feet long and 8 feet wide. Well, four, 6, and 8. All right. So highlighting a change. Four times four equals 16. Four times 6. It equals 24. And four times 8. Equals 32. What are we increasing about? 24 -16 equals 8. So we're increasing about 8. Feet. I'm sorry, square feet. Each time. So let's look at number four. And Jacob has a rectangular garden with an area of 56 ft². The link to the garden is 8 ft². What is the width of the garden? Well, using array of unit squares. Well then I would draw. And. This way. Until I got to 56. Now, there's a quicker way. If you remember, 56 divided by 8. What is 56 divided by 8? Yeah. 7. The answer is 7. Feet. Once we get that written down, we can turn the next page.