Question

during a renovation project for the train station, a parking lot for commuter train passengers is being enlarged. the original lot has an area of 9600 yd², and it is being enlarged by a scale factor of 3. what is the area of the new parking lot? enter your answer in the box. yd²

Explanation:

Step1: Recall the area - scale factor relationship

When a two - dimensional figure is scaled by a scale factor \(k\), the area of the new figure is \(k^{2}\) times the area of the original figure. Here, \(k = 3\).

Step2: Calculate the area of the new parking lot

Let \(A_{o}=9600\space yd^{2}\) be the area of the original parking lot. The area of the new parking lot \(A_{n}\) is given by the formula \(A_{n}=A_{o}\times k^{2}\). Substitute \(A_{o}=9600\) and \(k = 3\) into the formula:

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Answer:

\(86400\)