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# Area word problem: house size

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.