On a floor plan drawn at a scale of 1:100, the area of a rectangular room is 30cm^2. What is the actual area of the room?

Question

Answer: 30 m^2

Just need help understanding the concept and putting it all together. I can't grasp it very well from the book. Please & Thanks for your time

Answer 1

if the scale is a:b (in this case 1:100), then the area is of scale a^2:b^2 (in this case, 1:100^2; or 1 to 10,000)

so if the scale area is 30cm^2, the real area is 30*10,000 cm^2
now the units: 100cm=1m
and in area (100cm)^2=1m^2 or
10,000 cm^2=1m^2
so a real area of 30x10,000cm^2= 1 m^2

Answer 2

Thanks Bob

Answer 3

30m^2

Answer 4

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Answer 5

1:100
One square = 30cm
100 squares = 3,000cm
100cm = 1m
Therefore the answer is 30m^2