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## Lesson 11: Scales without units

# Interpreting a scale drawing

CCSS.Math:

## Video transcript

Maya and Mabel are
inspecting a 80 to 1 scale floor plan
of their new house. The dimensions of the living
room in the scaled plan are 4 centimeters by 5
centimeters right over here. What is the area of the
living room in the real world? So they gave us these
dimensions right over here. This is the scale
plan, and then we could figure out these
dimensions in the real world by looking at the scale
factor right over here. It's an 80 to 1
scale floor plan. And we can assume
that the house is much bigger than the floor plan. So the 80, for every
80 units in the house, that represents 1 unit
on the floor plan. So if we had 80
meters in the house, that would be represented as
1 meter on the floor plan. If we had 80 centimeters
in the house, that would be represented by 1
centimeter in the floor plan. And it goes the
other way around. 1 centimeter on the
floor plan would represent 80 centimeters
in the house. And it's always important to
do-- if this confuses you, just always do a reality check
that the house should be bigger than the floor plan. So if the floor plan for this
dimension of our living room is 4 centimeters, the actual
house will be 80 times that. And 80 times 4 is 320-- let
me do that in a blue color-- is equal to 320 centimeters. And we can do the same thing for
the length of the living room. So 80 times 5
centimeters is going to get us to-- is going to be--
80 times 5 is 400 centimeters. So we could figure out
the area of this room in centimeters, if we
like, and I guess, why not? It might be easier to
convert it to meters later. So let's see, 400 centimeters
times 320 centimeters. Let me write this down. 400 times 320. Let's think about it. 4 times 32 is going to
be 120, plus 8, 128. And I have 1, 2, 3 zeroes. 1, 2, 3. So it's going to be 128,000
centimeters squared. Now that's a lot of
square centimeters. What would we do if we wanted
to convert it into meters? Well, we just have to figure out
how many square centimeters are there in a square meter. So let's think
about it this way. A meter is equal to-- 1 meter
is equal to 100 centimeters. So a square meter, so
that's right over there. 1 meter squared would be
1 meter by 1 meter, which is the same thing as 100
centimeters by 100 centimeters. And so if you were to calculate
this area in centimeters, 100 times 100 is 10,000, is
equal to 10,000 centimeters squared. So you have 10,000
square centimeters for every square meter. And so, if you want to convert
128,000 centimeters squared to meters squared, you
would divide by 10,000. So dividing that by 10,000 would
give us 12.8 square meters. Now, another way you
could've done it, and maybe this would
have been easier, is to convert it up here. Instead of saying
400 centimeters times 320 centimeters,
you would say, well, 400 centimeters, that's
going to be 4 meters. And 320 centimeters,
well, that's 3.2 meters. And you would say,
OK, 4 times 3.2, that is 12.8 square meters. But either way, the
area of the living room in the real world in meters
squared, or square meters, is 12.8.