A map of the United States of America has a scale of $1 : 8\,000\,000$.

1. Convert the actual length from kilometres to centimetres and apply the map scale.

Scale $1:8\,000\,000$ means

$1\text{ cm on map}=8\,000\,000\text{ cm actual}$.

Actual length of river:

$3766\text{ km}=3766\times 100\,000=376\,600\,000\text{ cm}$

Map length:

$\dfrac{376\,600\,000}{8\,000\,000}=47.075\text{ cm}$

1. Find the actual area represented by $66.25\text{ cm}^2$ using the area scale.

Scale $1:8\,000\,000$ means
$1\text{ cm}$ on the map represents $8\,000\,000\text{ cm}$ actually.

So
$1\text{ cm}^2\text{ on the map represents }(8\,000\,000)^2\text{ cm}^2\text{ actually}.$

Actual area
$=66.25\times (8\,000\,000)^2\text{ cm}^2.$

2. Convert the actual area from square centimetres to square kilometres.

Since $1\text{ km}=100\,000\text{ cm}$,
$1\text{ km}^2=(100\,000)^2=10^{10}\text{ cm}^2.$

Hence
$\frac{66.25\times (8\,000\,000)^2}{10^{10}}=424\,000\text{ km}^2.$