Proportion problem: The scale of a map is 1 : 20 000 What area does 8 cm2 represent?

[MathsFormula]

The scale of a map is 1 : 20 000

What area does 8 cm² represent?

Answer in book is 0.32 km² (or 320 000 m²)


My working:

1 cm is 20000 cm so 8 cm is 160000 cm

This is 1600 m .... which is 1.6 km

So answer is 1.6 km² WRONG ANSWER


Please help. Thanks

 

[Deleted member 4993]

The scale of a map is 1 : 20 000

What area does 8 cm² represent?

Answer in book is 0.32 km² (or 320 000 m²)


My working:

1 cm is 20000 cm so 8 cm is 160000 cm

This is 1600 m .... which is 1.6 km

So answer is 1.6 km² WRONG ANSWER


Please help. Thanks

1cm ≡ 2 * 10⁴ cm (scaled) = 2 * 10^-1 km

1 cm² ≡ 4 * 10^-2 km² (scaled)

8*1 cm² ≡ 8*4 * 10^-2 km² (scaled)

 

[stapel]

The scale of a map is 1 : 20 000

What area does 8 cm² represent?

Answer in book is 0.32 km² (or 320 000 m²)


My working:

1 cm is 20000 cm so 8 cm is 160000 cm

This is 1600 m .... which is 1.6 km

So answer is 1.6 km² WRONG ANSWER

How did you get from "1.6 km" (a measure of length) to "1.6 km²" (a measure of area)? In other words, you squared the measurement unit; why did you do nothing with the numerical portion?

 

[MathsFormula]

1cm ≡ 2 * 10⁴ cm (scaled) = 2 * 10^-1 km

1 cm² ≡ 4 * 10^-2 km² (scaled)

8*1 cm² ≡ 8*4 * 10^-2 km² (scaled)

Thanks for that. Helped alot

 

[MathsFormula]

How did you get from "1.6 km" (a measure of length) to "1.6 km²" (a measure of area)? In other words, you squared the measurement unit; why did you do nothing with the numerical portion?

I was messing about with square roots. I thought because area is being analysed I needed to square root the area to find out the length of each side then use the scale information

1cm ≡ 2 * 10⁴ cm (scaled) = 2 * 10^-1 km

1 cm² ≡ 4 * 10^-2 km² (scaled)

8*1 cm² ≡ 8*4 * 10^-2 km² (scaled)

In his explanation Mr Khan did not square root anything. Don't understand why not when the scale is meant for straight lines not areas.

I was square rooting the '8'