Question

scale: 1 inch : 4 miles. what is the actual area of the town? blueprint area 3.5 in². actual area ? mi²

Explanation:

Step1: Find the scale - factor for area

The linear scale is 1 inch : 4 miles. For area, the scale - factor is the square of the linear scale - factor. Since the linear scale factor is $k = 4$ (where 1 inch on the blueprint represents 4 miles in reality), the area scale - factor is $k^{2}=4^{2}=16$ square miles per square inch.

Step2: Calculate the actual area

Multiply the blueprint area by the area scale - factor. The blueprint area is $A_{blueprint}=3.5$ in². The actual area $A_{actual}=A_{blueprint}\times k^{2}$. So, $A_{actual}=3.5\times16$.
$A_{actual}=56$ mi²

Answer:

56