Question

the scale factor of the blueprint of a wall to the actual wall is 0.07. the area of the actual wall is 36 ft². what is the area of the wall on the blueprint?
0.252 ft²
0.07 ft²
0.01764 ft²
0.1764 ft²

Explanation:

Step1: Recall area scale factor rule

For similar figures, the ratio of areas is the square of the ratio of corresponding linear dimensions (scale factor). Let the scale factor be \( k = 0.07 \), actual area \( A_{actual}=36\space ft^2 \), and blueprint area \( A_{blueprint} \). The formula is \( A_{blueprint}=k^2\times A_{actual} \).

Step2: Calculate \( k^2 \)

\( k^2=(0.07)^2 = 0.0049 \)

Step3: Find blueprint area

Multiply \( k^2 \) by actual area: \( A_{blueprint}=0.0049\times36 \)
\( 0.0049\times36 = 0.1764 \)

Answer:

\( 0.1764\space ft^2 \) (corresponding to the option: 0.1764 \( ft^2 \))