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So the area of the map is 2000 hectares but the question is asking to find the area of the farm in cm2. I'm a bit confused as how to work this out. I know that 1 hectare is equals to 10,0000 m2.

The scale of the map is 1: 180,000

lase
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  • Do you know how to convert hectares to square meters? You stated that you do. Do you know how to convert square meters to square centimeters? That should be obvious. – MPW Sep 13 '14 at 02:09

1 Answers1

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An hectare is $10^4$ square metres. A square metre is $(100)^2=10^4$ square cm. So the field has $2\times 10^{11}$ square cm.

The linear scale is $180000$ to $1$. So $1$ square cm on the map represents $(180000)^2$ square cm on the ground.

Thus on the map, the area of the farm is $\frac{10^{11}}{(180000)^2}$ square cm.

Remark: If the linear dimensions of an object are scaled by the scale factor $\lambda$, then area is scaled by the factor $\lambda^2$, and volume is scaled by the factor $\lambda^3$. In our case, $\lambda=\frac{1}{180000}$.

André Nicolas
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