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### Course: 3rd grade (Eureka Math/EngageNY) > Unit 4

Lesson 4: Topic D: Applications of area using side lengths of figures- Decomposing shapes to find area: grids
- Understand decomposing figures to find area
- Decomposing shapes to find area: subtract
- Decomposing shapes to find area: add
- Decompose figures to find area
- Area word problem: house size
- Comparing areas of plots of land
- Compare areas by multiplying

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# Area word problem: house size

Sal decomposes an irregular shape to find area of entire figure. Created by Sal Khan.

## Want to join the conversation?

- In the video on calculating the square footage of a house, at2:50how did you get the width of the green rectangle to be 25ft? Shouldn't it be 26ft, the same as the width of the blue one?(58 votes)
- At3:07, why did we not include the 5? Is it because it did not have a rectangle to contribute to the problem in order to calculate the total area?(16 votes)
- The video didn't include the 5 because it is showing the length of the distance between the teal rectangle and the purple one. The purple rectangle already show the length and width(20 and 20). The 5 is also not the whole length of the rectangle. It is trying to throw you off.(22 votes)

- Maybe some of the confusion comes from the issue that many Third Graders have not yet learned how to multiply two, two digit numbers together (unless they are multiples of 10). My nephew was only able to calculate 20ft x 20ft so could not complete the above problem. The Third Grade multiplication section of this site only includes lessons on multiplying single digit multiplication problems so possibly this problem is advanced for the typical Third Grader?(7 votes)
- it is not to complicated because 6,555*6,555=42968225(8 votes)

- Why are you using a house as the example?(8 votes)
- because if you are a landscaper then you know how long your walls have to be or were the rooms would be, so thats probably why(2 votes)

- Why would you have an instructional video showing how to find the area of a house and then not have any practice problems following? I assume that to find the house size, one would have to apply both the addition and subtraction decomposition?(9 votes)
- because your mom is so stupid she can't even understand a simple explanation(0 votes)

- How does area Help us in the real world?(3 votes)
- Area helps you in the real world for construction projects, such building houses(shown in the video), for carpeting in your home, etc.(8 votes)

- How can I find the area of the House? I tried, but Igot it wrong.

:((5 votes)- It is in the video,we have to break it in different rectangles.(4 votes)

- I dont understand1:30on how it's 15 ft(6 votes)
- find the length, width and perimeter of a room with an area measures 18.50 square meter?(4 votes)
- You need to be more specific. There are multiple answers to this question.

Here are a few (some of the more practical ones):

7.4m x 2.5m

9.25m x 2m

4.625m x 4m(5 votes)

- hey Sal, i thought the shape in pink is a square not a rectangle?(4 votes)
- A square is a certain kind of rectangle. A rectangle has four sides, two pairs of equal, parallel sides, and four right angles. A square fits this criteria.(4 votes)

## 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.