The map of a park is drawn to a scale of 1: n. A garden, which has an actual area of 0.32 km^2, is represented by an area of 2 cm^2 on a map.

1. Convert the actual area into square centimetres.

$0.32\text{ km}^2 = 0.32 \times (100\,000)^2\text{ cm}^2$

$= 3\,200\,000\,000\text{ cm}^2$

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

Map area : actual area

$2 : 3\,200\,000\,000 = 1 : 1\,600\,000\,000$

Since the map scale is $1:n$, the area scale is $1:n^2$.

$n^2 = 1\,600\,000\,000$

$n = \sqrt{1\,600\,000\,000} = 40\,000$

1. Use the scale from part (a) to convert the map distance to the actual distance.

From part (a), the scale is $1:4000$.
So $5\text{ cm}$ on the map represents
$5 \times 4000 = 20000\text{ cm}$ in actual distance.
Since $100\text{ cm} = 1\text{ m}$,
$20000\text{ cm} = 200\text{ m}.$