A map is drawn to a scale of 1:10 000. On the map, the Gauss Forest occupies a rectangular region measuring $10 \mathrm{~cm}$ by $100 \mathrm{~cm}$. What is the actual area of the Gauss Forest, in $\mathrm{km}^{2}$ ?
(A) 100
(B) 1000000
(C) 1000
(D) 1
(E) 10
A map is drawn to a scale of 1:10 000. On the map, the Gauss Forest occupies a rectangular region measuring $10 \mathrm{~cm}$ by $100 \mathrm{~cm}$. What is the actual area of the Gauss Forest, in $\mathrm{km}^{2}$ ?
(A) 100
(B) 1000000
(C) 1000
(D) 1
(E) 10

## Solution

The actual lengths of the sides of the Gauss Forest are 10000 times the lengths of the sides on the map. So the one side has length

$$
10000 ¥ 10 \mathrm{~cm}=100000 \mathrm{~cm}=1000 \mathrm{~m}=1 \mathrm{~km}
$$

and the other side has length

$$
10000 ¥ 100 \mathrm{~cm}=1000000 \mathrm{~cm}=10000 \mathrm{~m}=10 \mathrm{~km}
$$

The actual area of the Gauss Forest is therefore $1 \mathrm{~km} ¥ 10 \mathrm{~km}=10 \mathrm{~km}^{2}$.