一处面积为 225 km^2 的森林保护区在地图上表示的面积为 36 cm^2。

1. Convert the actual area from square kilometres to square centimetres.

Since $1\text{ km}=100000\text{ cm}$,

$1\text{ km}^2=(100000)^2\text{ cm}^2=10^{10}\text{ cm}^2$

$225\text{ km}^2=225\times 10^{10}\text{ cm}^2=2\,250\,000\,000\,000\text{ cm}^2$

2. Use the area scale to find the linear scale factor $n$.

Map area : actual area

$36:2\,250\,000\,000\,000$

For a map scale of $1:n$, the area scale is $1:n^2$.

So

$\frac{36}{2\,250\,000\,000\,000}=\frac{1}{n^2}$

$n^2=\frac{2\,250\,000\,000\,000}{36}=62\,500\,000\,000$

$n=\sqrt{62\,500\,000\,000}=250000$

1. Use the map scale to find the actual distance and convert it to kilometres.

From part (a), the scale is $1:250000$.\n\nActual distance represented by $2.1\text{ cm}$\n$=2.1\times 250000\text{ cm}$\n$=525000\text{ cm}$\nSince $100000\text{ cm}=1\text{ km}$,\n$525000\text{ cm}=5.25\text{ km}$