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Sal decomposes an irregular shape to find area of entire figure. Created by Sal Khan.
Video transcript
You are thinking about buying a house, but you really want to figure out how much area does the house cover. What is the square footage of the house? Or what is the area of the foundation of the house? So right here, we have the floor plan of the house. And you're tasked with finding its area. And you're given the dimensions of a bunch of walls of the house. This wall right here is 18 feet. This is 8 feet. This is 20 feet, 20 feet, 5 feet, 26 feet, 15 feet, and 25 feet. But you're a little confused. You know how to find the area of rectangles, but how do you find an area of a strange shape like this? So I encourage you to pause this video and try to figure out the area of this strange house footprint shape, floor plan shape, using the techniques that you already know about. So what you already do know about is how to find the area of rectangles. So if we can break this house's floor plan into a series of rectangles and find out the areas of those rectangles, then we can figure out the area of this entire house. So let's break it into a bunch of simpler rectangles. So I could have one rectangle here. It has a width of 20 feet, and it has a length of 20 feet. So that would be a rectangle right over there. We should be able to figure out its area. Then I could set up another rectangle that has a width of 26 feet and has a length. That's its length right over there. And we could think about in a second what that length actually is. Actually, let's think about that. How would we figure out what this length actually is? Well, this length plus 5 feet is going to be the same thing as this length over here. It's the same as the opposite wall of this rectangle. So this length plus 5 feet is 20 feet. Well, this must be 15 feet. So this blue rectangle is 15 feet long and 26 feet wide. Now let's add another rectangle. We could have one that's 18 feet long and then goes the entire length of the house. Goes the entire length of the house like that. And you might say, wait, how do we figure out its width? How do we figure out the width of this rectangle? Well, we know that this is 8 feet. We know that this is 20 feet, and we know that this is 26 feet. So the entire width is going to be 26 feet plus 20 feet. So 26 plus 20 gets us to 46. Plus 8 gets us to 54 feet. So this is 54 feet right over here. Did I do that right? Let's see. 8 plus 36 would be 34, plus 20 is 54 feet. And then finally we have one last rectangle to deal with, this rectangle right over here, which is 15 feet long and 25 feet wide. And so now we can calculate the areas of the different rectangles. So the total area is going to be the 20 feet by the 20 feet. So let's just multiply them. So it's going to be 20 times 20. That's this area right over here. Plus 15 times 26. That's this area right over there. Plus 18 times 54, which is this area right over there. And then finally, plus 15 times 25, which is this area right over here. So we just have to now evaluate these things. So what is 20 times 20? Well, this is going to be 400. What's 15 times 26? Well, let's multiply it out. 26 times 15. 6 times 5 is 30. 2 times 5 is 10, plus 3 is 13. Now I'm going to multiply a 10 times 26, gets us to 260. And you add these two together. You get 390. So it's 400 plus 390. Now we've got to multiply 18 times 54, or 54 times 18. So let's do that. 54 times 18. 8 times 4 is 32. 8 times 5 is 40, plus 3 is 43. Now we're multiplying this 10 times 54. Gets us to 540. And we add. 2 plus 0 is 2. This 30 plus the 40 gets us to a 70. In other words, a 3 plus a 4 in the tens place. And then 400 plus 500 is 900. So we get to 972. And one more of these multiplications. 25 times 15. And actually, we could do that in our head. This is 26 times 15, so 25 times 15 is going to be this minus 15. So it's going to be 300. Let's see, if you subtract 10, you get to 380. Subtract another 5, 375. Let me do it in that same color. So plus 375. And now let's add up these numbers. So we have 375 plus 972, plus 390, plus 400. And so this gets us to 5-- this is the home stretch. We deserve a drum roll now. 5 plus 2 is 7. 7 plus 7 is 14, plus 9 is 23. 2 plus 3 is 5, plus 9 is 14, 17, 21. So the square footage of this house? 2,137 square feet.