Question

scale: 1 inch : 3 miles. what is the actual area of the lake? actual area ? mi². blueprint area 4.5 in²

Explanation:

Step1: Find the scale - factor for area

The linear scale is 1 inch : 3 miles. For area, the scale - factor is the square of the linear scale - factor. The linear scale factor $k = 3$ (since 1 inch represents 3 miles), so the area scale factor $k^{2}=3^{2}=9$ square miles per square inch.

Step2: Calculate the actual area

Multiply the blueprint area by the area scale - factor. The blueprint area is $A_{blueprint}=4.5$ in². The actual area $A_{actual}=A_{blueprint}\times k^{2}$. So $A_{actual}=4.5\times9$.
$A_{actual}=40.5$ mi²

Answer:

$40.5$