## Calculating the square footage of a house

you really want to figure out how much

area does a house cover what is the the

square footage of the house or what is

the 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 look prints shape for

plan shape using the techniques that you

do know about is how to find the area of

rectangles so if we can break this

houses floorplan 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 and 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 this length plus 5

feet is going to be the same thing as

this length over here is the same as the

opposite wall of this 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

246 plus 8 gets us to 54 feet so this is

54 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 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 so plus

15 times 26 that's this area right over

there

plus 18 times 54 plus 18 times 54 which

is this area right over there and then

finally plus 15 times 25 plus 15 times

25 which is this area 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 let's multiply it out

26 times 15 6 times 5 is 30 2 times 5 is

10 plus 3 is 13 and 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

three is 43 now we're multiplying this

10 times 54 gives us to 540 and we add 2

plus 0 is 2

this 30 plus the 40 gets us to a 70 it's

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 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 to see if you

subtract 10 you get 2 380 subtract

another 5 375 and let me do it in that

same color so plus plus 375 and I'll set

up these numbers so we have 375 plus 972

plus three hundred and ninety 390 plus

400 plus 400 and so this gets us to five

and this is the homestretch 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 2137

square square feet