A map has a scale of 1 : 150 000.

1. Use the scale to find the actual length in centimetres.

Scale $1:150\,000$ means $1\text{ cm}$ on the map represents $150\,000\text{ cm}$ in actual distance.

For $6.4\text{ cm}$ on the map,
$6.4\times150\,000=960\,000\text{ cm}$

2. Convert the actual length from centimetres to kilometres.

Since $100\,000\text{ cm}=1\text{ km}$,
$960\,000\text{ cm}=\frac{960\,000}{100\,000}=9.6\text{ km}$

1. Find the actual area represented by $1\text{ cm}^2$ on the map.

Scale $1:150000$ means
$1\text{ cm}$ on map represents $150000\text{ cm}=1.5\text{ km}$ actual.

Hence
$1\text{ cm}^2 \text{ on map represents } (1.5)^2=2.25\text{ km}^2 \text{ actual}.$

2. Divide the actual area by the area represented by $1\text{ cm}^2$ to find the map area.

Map area
$=10.125\div 2.25=4.5\text{ cm}^2.$