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 $k = 4$, the area scale factor $k^{2}=4^{2}=16$ (because if the lengths are in the ratio $a:b$, the areas are in the ratio $a^{2}:b^{2}$).

Step2: Calculate the actual area

The blueprint area is $A_{blueprint}=3.5$ in². To find the actual area $A_{actual}$, we multiply the blueprint area by the area scale - factor. So $A_{actual}=A_{blueprint}\times k^{2}$. Substituting the values, we get $A_{actual}=3.5\times16$.
$A_{actual}=56$ mi²

Answer:

56