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Measurement & Data - Statistics & Probability 189-200

Course: Measurement & Data - Statistics & Probability 189-200>Unit 1

Lesson 3: Area formula intuition

Counting unit squares to find area formula

Sal uses unit squares to see why multiplying side-lengths can also find the area of rectangles.    Created by Sal Khan.

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• Does it matter if it's a rectangle or a square in area? Wouldn't it still be length times width?
(46 votes)
• That's true. The only thing is, when calculating the area of a square, you can simply multiply one of the sides by itself, since you know the other sides are all the same.
(21 votes)
• Could I use this information for inches as well?
(26 votes)
• Yeah. If you do the same thing, but change the measurement, you can do the same thing for inches like you did with meters.
(26 votes)
• Hi Khan, My name is Wyatt and I live in Vancouver British Columbia. I hope that all of Khan is well during this crazy time of CV19. I have a math/space problem that needs solving. I am hoping that you would kindly help me out. I own a yoga studio in Vancouver. The province is slowly letting small businesses open with restrictions. I am measuring the studio space later today and will have accurate numbers of what the square footage of the floor space is. What i need to do in the space to make it safe is go from a capacity of 100 people to 29 people. So, I need to fit 29 yoga mats in this space in an off center pattern. For example - the lay out would look like the off set dots on a dice of 5 dots. That pattern would be repeated within the space to make up 29 spaces or 29 yoga mats at equal distance apart. If I send you a drawing of the space would you be able to reconfigure the space to accommodate 29 yoga mats. I will also provide the size of the Yoga mat. What do you think of this ? Is there an instructor out there that can connect with me and help me solve this spacial math problem.
(16 votes)
• you must have peace in your house cause my house is 0% peaceful and only peaceful when my dad takes me on hikes or nature walks
(0 votes)
• how do people know the perimeter of a circle? I'm confused..
(7 votes)
• The perimeter of a circle is called the circumference. It is π multiplied by the diameter of the circle. And since the diameter is twice the radius, you could also say that C=πd=2πr. If you want to approximate π, use 3.14
(20 votes)
• how do you write with your mouse? it's so cool!
(9 votes)
• what is 1000 times 1000=10000
(5 votes)
• 1 million
(8 votes)
• can i use this information for finding area in triangles?
(3 votes)
• No, you use area by multiplying base times height, then divide by 2 by using square units.
(7 votes)
• i love khan acdamy
(8 votes)
• Do we have to wright out square to show our work or can we just do sq?
(6 votes)
• If a rectangle has width of 0.5cm and length of 0.6cm does the area equal to 0.3cm^2? and if it's true, how is this area less than width and length?
(4 votes)
• Yes. That's right and thought-provoking. You can't really compare the length or width to the area. One is cm and the other is cm^2. It's impossible to say if a pencil is longer than an hour. It's asking you to compare time to length, which isn't possible. The same thing happens in this case.
(4 votes)

Video transcript

I've got three rectangles here, and I also have their dimensions. I have their height and their width. And in fact, this one right here has the same height and width, so this is actually a square. So let's think about how much space they each take up on my screen. And since we're doing everything in terms of meters, since all of the dimensions are in meters, I'm going to measure the area in terms of square meters. So let's see how many square meters I can fit onto this yellow rectangle without going outside of its boundary and without overlapping. So I can fit 1 square meter. Remember, a square meter is just a square where its length is 1 meter and its width is 1 meter. So that's 1 square meter, 2, 3, 4, or 5, and 6 square meters. So we see here that the area is 6 square meters. Area is equal to 6 square meters. But something might be jumping out at you. Did I really have to sit and count 1, 2, 3, 4, 5, 6? You might have recognized that I could view this as really 2 groups of 3. And let me make that very clear. So, for example, I could view this as one group of 3 and then another group of 3. Now, how did I get groups of 3? Well, that's because width here is 3 meters. So I could put 3 square meters side by side. And how did I get the 2 groups? Well, this has a length of 2 meters. So another way that I could have essentially counted these six things is I could have said, look, I have a length of 2 meters. So I'm going to have 2 groups of 3. So I could multiply 2 times 3, 2 of my groups of 3, and I would have gotten 6. And you might say, hey, wait. Is this just a coincidence that if I took the length and I multiplied it by the width, that I get the same thing as its area? And no, it's not, because when you took the length, you essentially said, well, how many rows do I have? And then you say when you multiply it by the width, you're saying, well, how many of these square meters can I fit into a row? So this is really a quick way of counting how many of these square meters you have. So you could say that 2 meters multiplied by 3 meters is equal to 6 square meters. Now, you might say, hey, I'm not sure if that always applies. Let's see if it applies to these other rectangles right over here. So based on what we just saw, let's take the length, 4 meters, and multiply by the width, and multiply by 2 meters. Now, 4 times 2 is 8. So this should give us 8 square meters. Let's see if this is actually the case. So 1, 2, 3, 4, 5-- and you see it's going in the right direction-- 6, 7, and 8. So the area of this rectangle is, indeed, 8 square meters. And you could view this as 4 groups of 2. So you could literally view this as 4 groups of 2. That's where the 4 times 2 comes from. So you could view it as 4 groups of 2 like this. Or you could view it as 2 groups of 4, So 1 group of 4 right over here. So you could view this is 2 times 4, and then 2 groups 4. I want to draw it a little bit cleaner. Now, you could probably figure out what the area of this rectangle is. It's actually a square, because it has the same length and the same width. We multiply the length, 3 meters, times the width, so times 3 meters, to get 3 times 3 is 9-- 9 square meters. And let's verify it again just to feel really good about this multiplying the dimensions of these rectangles. So we have 1, 2, 3, 4, 5, 6, 7, 8, and 9. So it matches up. We figure out how many square meters can we cover this thing with, without overlapping, without going over the boundaries. We get the exact same thing as if we multiplied 3 times 3, if we multiplied the length times the width in meters.