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Polygon is a scaled copy of Polygon using a scale factor of .How many times as large is the area of Polygon compared to the area Polygon ?
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Q. Polygon is a scaled copy of Polygon using a scale factor of .How many times as large is the area of Polygon compared to the area Polygon ?
- Denote Area of Polygons: Let's denote the area of Polygon C as and the area of Polygon D as . When a figure is scaled by a scale factor, the area is scaled by the square of the scale factor. Since Polygon D is a scaled copy of Polygon C using a scale factor of , we can write the relationship between their areas as .
- Calculate Scale Factor: The scale factor given is . To find out how many times larger the area of Polygon D is compared to Polygon C, we need to square the scale factor: .
- Compare Areas: Therefore, the area of Polygon D is times larger than the area of Polygon C. This is because when scaling a two-dimensional figure, the area scales by the square of the scale factor.
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