The scale of a map is 1 : n.
A school garden measuring 8 cm^2 on a map has an actual area of 2048 m^2.
Find n. Answer n = ...

1. Convert the actual area from square metres to square centimetres.

Since $1\text{ m}^2 = 10\,000\text{ cm}^2$,
$2048\text{ m}^2 = 2048 \times 10\,000 = 20\,480\,000\text{ cm}^2.$

2. Relate the map area to the actual area using the area scale factor.

The map scale is $1:n$, so
$\text{area scale} = 1^2:n^2.$
Given $8\text{ cm}^2$ on the map represents $20\,480\,000\text{ cm}^2$ actual area,
$\frac{20\,480\,000}{8}=n^2$
$n^2=2\,560\,000$
$n=\sqrt{2\,560\,000}=1600.$