The scale of a map is 2 cm to 1 km.

1. Apply the map scale to convert actual distance to map length

Since $1\text{ km}$ is represented by $2\text{ cm}$ on the map,

$8.5\text{ km} \text{ is represented by } 8.5 \times 2 = 17\text{ cm}.$

1. Convert the given linear scale into an area scale

The scale is $2\text{ cm} : 1\text{ km}$.

So
$2\text{ cm} \times 2\text{ cm} \text{ on the map represents } 1\text{ km} \times 1\text{ km} \text{ actual}.$

Hence,
$4\text{ cm}^2 \text{ on the map represents } 1\text{ km}^2 \text{ actual}.$

2. Use the area scale to find the actual area represented by $9\text{ cm}^2$

Since $4\text{ cm}^2$ represents $1\text{ km}^2$,
$9\text{ cm}^2 \text{ represents } \frac{9}{4}\text{ km}^2.$

$\frac{9}{4}=2.25$