Question
2. A figure is dilated by a factor of 5 . By what factor will the area of the figure change? 1 5 10 25
Ask by Simmons Gough. in the United States
Feb 03,2025
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The area of the figure will change by a factor of 25.
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When a figure is dilated by a scale factor, the area of the figure changes by the square of that scale factor. So, if the figure is dilated by a factor of 5, the area will change by \(5^2\), which equals 25. Therefore, the area of the figure will increase by a factor of 25. This is a neat aspect of geometry: as you scale up (or down) a shape, while the dimensions change linearly, the area changes quadratically! Just imagine inflating a balloon – it grows in size much faster than the initial stretch of the rubber!
