Figure out the area of a field with a scale.

Question

The scale on a map is 1:50,000. The area of a field on the map is 1.2 square centimetres. Calculate the actual area of the playing field in square kilometres.

Here I thought you would multiply 50,000 by 1.2 to get 60,000 (the actual size of the playing field in square centimetres). Then divide his by 100 to get it in m² (600m²) then divide by 1000 for km² (0.6 km², I’m just spelling it out here for ease of seeing working). Therefore it is 0.6 km² in real life but the answer says 0.3km². I don’t understand how they got this answer and I would be extremely surprised if they were incorrect as this is a past paper. Any assistance would be GREATLY appreciated.

Answer 1

1.2 cm^2 x 50,000

= 60,000 cm^2 there's 100^2 = 10,000 cm^2 in a square meter

= 60,000/10,000 = 6 square meters. a square meter is 1 m by 1 m. which is 100 cm by 100 cm = 10,000 square centimetres

1000^2 m = 1 km

6/1000000 = 0.000006 km^2 = 6 x 10^6 km^2 in scientific notation

60,000 cm^2 = 6 m^2 = 0.000006 km^2

You're right, 0.3 km^2 is incorrect

6 square meters could be a field 6 m by 1 m, or 3m by 2m. That's the only way a "3" might show up. If the field were 6 by 1, then 50,000 times 6 cm = 300,000 cm. Divide by 100 that's 3000 meters. that converts to 3 km. which is sort of closer to .3 km^2.

Or maybe the problem didn't read "1.2" but "1:2" cm. the field map had it as 1 cm by 2 cm which would have an area of 2 cm^2. then 50,000 x 2 = 100,000 cm^2 = 10 m^2 = 0.00001 km^2. Still no "3" though. But some similar typo might give you a different answer. "1:2" might also mean 1/(1+2) = 1/3. the 3 and 6 aren't that close on a keyboard. Guess is there's a typo in the problem or the solution. Maybe it's the correct answer to a different but similar problem and they got mixed up.

or try working backwards: 0.3 km^2 = 100,000 x .3 m^2 = 30,000 m^2

convert to cm^2. multiply by 10,000 which is 300 million cm^2 or 3.0 x 10^8 cm^2

That doesn't seem to lead anywhere.