A length of 5 cm on a map represents an actual distance of 2.5 km. Find

1. Find the scale factor from 5 cm to 20 cm on the map and apply it to the actual distance.

$20 \div 5 = 4$

Actual distance $= 2.5 \times 4 = 10$ km

1. Convert the actual distance to centimetres so both distances are in the same unit.

$2.5\text{ km}=2.5\times 100000\text{ cm}=250000\text{ cm}$

So $5\text{ cm}$ on the map represents $250000\text{ cm}$ in actual distance.

2. Divide both parts of the ratio by 5 to write the scale in the form $1:n$.

Map : actual

$=5:250000$

$=1:50000$

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

From the given scale, $5\text{ cm}$ represents $2.5\text{ km}$.

So $1\text{ cm}$ represents
$\frac{2.5}{5}=0.5\text{ km}$.

Hence $1\text{ cm}^2$ represents
$(0.5)^2=0.25\text{ km}^2.$

2. Multiply by $30$ to find the actual land area represented by $30\text{ cm}^2$.

Actual land area represented by $30\text{ cm}^2$ is
$30\times 0.25=7.5\text{ km}^2.$