A map has a scale of 1 : 50 000.

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

Scale $1:50\,000$ means $1\text{ cm}$ on the map represents $50\,000\text{ cm}$ in actual distance.

Actual distance
$=7.5\times 50\,000=375\,000\text{ cm}$

Since $100\,000\text{ cm}=1\text{ km}$,
$375\,000\text{ cm}=3.75\text{ km}$

1. Convert the actual area into square centimetres.

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

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

$2.25\text{ km}^2=2.25\times(100000)^2\text{ cm}^2$

2. Apply the area scale factor to find the map area.

The map scale is $1:50000$, so

$\text{map area}:\text{actual area}=1^2:50000^2$

$\text{map area}=\frac{2.25\times(100000)^2}{50000^2}$

$=2.25\times\left(\frac{100000}{50000}\right)^2$

$=2.25\times 2^2=9$

So the area of the lake on the map is $9\text{ cm}^2$.