Question

andrea made a replica of the empire state building. the surface area of the model is 45 feet². what is the surface area of the actual empire state building in ft.² if the scale factor is 44? enter your answer as a whole number, with the appropriate unit, like this: 42 ft.^2

Explanation:

Step1: Recall area - scale - factor relationship

If the scale factor of two similar figures is \(k\), the ratio of their surface areas is \(k^{2}\).

Step2: Calculate the surface area of the actual building

Let \(A_1\) be the surface - area of the model and \(A_2\) be the surface - area of the actual building, and \(k\) be the scale factor. We know that \(\frac{A_2}{A_1}=k^{2}\), so \(A_2 = A_1\times k^{2}\). Given \(A_1 = 45\) square feet and \(k = 44\), then \(A_2=45\times44^{2}\).
\[

$$\begin{align*} A_2&=45\times44^{2}\\ &=45\times1936\\ & = 87120 \end{align*}$$

\]

Answer:

87120 ft.^2