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Current time:0:00Total duration:4:26

Interpreting a scale drawing

CCSS.Math:

Video transcript

Mayon mobile are inspecting a 80 to 1 scale floorplan of their new house the dimensions of the living room in the scaled plan are 4 centimeters 4 centimeters by 5 centimeters by 5 centimeters right over here what is the area 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 here it's an 80 to 1 scale floorplan and we can assume that the house is much bigger than the floor plan so the 80 for every 80 units in the house for every 80 units in the house that represents one unit on the floor planned 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 one centimeter in the floor plan so whatever what if it goes the other way around one centimeter on the floor plan would represent 80 centimeters in the house and it's always important to do if this confuses you just to 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 that blue color is equal to 300 and 20 centimeters 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 can figure out the area of this room in centimeters if we like it I guess we why not it might be easier to convert 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 for time 32 is going to be 120 +8 128 and I have one two three zeroes one two three so it's going to be a hundred and twenty eight thousand one hundred and twenty eight thousand centimeter squared 128 thousand centimeter 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 one meter is equal to 100 centimeters so a square meter a square meter so that's right over there one meter squared would be one meter by one meter which is the same thing as 100 centimeters by a hundred centimeters and so if you were to calculate this area in centimeters a hundred times 100 is ten thousand is equal to ten thousand ten thousand centimeters squared centimeters squared so you have ten thousand square centimeters for every square meter and so if you wanted to convert a 128 thousand centimeters squared to meter squared you would divide by ten thousand so dividing that by ten thousand would give us dividing it by ten thousand would give us 12 twelve point eight twelve point eight square meters now another way you could have done it and maybe this would have been easier is to convert it up here instead of saying 400 centimeters times 320 centimeters you say well 400 centimeters that's going to be four meters that's going to be four meters and 320 centimeters well that's 3.2 meters times 3.2 - and you say okay four times 3.2 that is twelve point eight square meters but either way the area of the living room in the real world in meter squared or square meters is twelve point eight