I'm having problem with this question :
A nature reserve of area $225 km^2$ is represented on a map by an area of $36 cm^2$Find the Representative Factor (R.F) of the map. What will the area of the nature reserve be on a map with a scale of $1cm$ to $5 km$.
Ans : $1:250000$, $9cm^2$
Looking forward for helpful answer. Thanks...
For the first question on one side we have $225\mathrm{km}^2=(15\cdot 15)\mathrm{km}^2=(15000\cdot 15000)\mathrm{m}^2=(1500000\cdot 1500000)\mathrm{cm}^2$ and on the other side $36\mathrm{cm}^2=6\cdot 6\mathrm{cm}^2$
So the ratio is $$6:1500000=1:250000$$
For the second question, we have the ratio $1\mathrm{cm}:5\mathrm{km}=1\mathrm{cm}:500000\mathrm{cm}=1:500000$, so what we need is just to map $225\mathrm{km}^2$ on this map. Again, $225\mathrm{km}^2=15\cdot 15\mathrm{km}^2$ and $15\mathrm{km}=1500000\mathrm{cm}$ are represented by $$1500000\mathrm{cm}\cdot 1/500000=3\mathrm{cm}$$
Finally, the area will be $$3\mathrm{cm}\cdot 3\mathrm{cm}=9\mathrm{cm}^2$$