The scale of a map is 4 cm : 1 km.

1. Convert the actual distance to centimetres and write the scale in common units.

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

$4\text{ cm}:1\text{ km}=4\text{ cm}:100000\text{ cm}$

2. Simplify the ratio so that the first term is 1.

Divide both sides by $4$:

$4:100000=1:25000$

1. Convert the map distance to the actual distance using the scale.

Since $4\text{ cm}$ on the map represents $1\text{ km}$ in actual distance,
$40\text{ cm} \div 4 = 10.$
So the actual distance is $10\text{ km}$.

1. Find the map area corresponding to $1\text{ km}^2$ using the given linear scale.

The scale is $4\text{ cm}:1\text{ km}$.

So an actual square of side $1\text{ km}$ is represented on the map by a square of side $4\text{ cm}$.

Hence,
$1\text{ km}^2 \text{ is represented by } 4^2=16\text{ cm}^2.$

2. Multiply by the actual area of the park to find the map area.

For an actual area of $4.5\text{ km}^2$,
$\text{map area}=4.5\times 16=72\text{ cm}^2.$