Question

the scale factor of the blueprint of a garage door to the actual garage door is 0.05. the area of the actual garage door is 220 ft². what is the area of the garage door on the blueprint? 5.5 ft² 55 ft² 11 ft² 0.55 ft²

Explanation:

Step1: Recall area - scale - factor relationship

If the linear - scale factor is $k$, the area - scale factor is $k^{2}$. Here, $k = 0.05$.

Step2: Calculate the area - scale factor

$k^{2}=(0.05)^{2}=0.0025$.

Step3: Find the area on the blueprint

Let $A_{b}$ be the area on the blueprint and $A_{a}$ be the actual area. We know that $\frac{A_{b}}{A_{a}}=k^{2}$. So $A_{b}=A_{a}\times k^{2}$. Given $A_{a} = 220$ ft², then $A_{b}=220\times0.0025$.
$A_{b}=0.55$ ft².

Answer:

$0.55$ ft²