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Polygon C has an area of 40 square units. Kennan drew a scaled version of Polygon C using a scale factor of (1)/(2) and labeled it Polygon D. What is the area of Polygon D ? square units

Polygon C C has an area of 4040 square units. Kennan drew a scaled version of Polygon C C using a scale factor of 12 \frac{1}{2} and labeled it Polygon D D .\newlineWhat is the area of Polygon D D ?\newlinesquare units

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Q. Polygon C C has an area of 4040 square units. Kennan drew a scaled version of Polygon C C using a scale factor of 12 \frac{1}{2} and labeled it Polygon D D .\newlineWhat is the area of Polygon D D ?\newlinesquare units
  1. Understand relationship scale factor: Understand the relationship between the scale factor and the area of similar polygons.\newlineWhen a polygon is scaled by a factor of kk, the area of the polygon is scaled by a factor of k2k^2. This is because area is a two-dimensional measurement, and scaling affects both dimensions (length and width).
  2. Calculate scale factor squared: Calculate the scale factor squared. Since the scale factor is 12\frac{1}{2}, we square it to find the factor by which the area will be scaled. (12)2=14\left(\frac{1}{2}\right)^2 = \frac{1}{4}
  3. Apply scale factor to area: Apply the scale factor squared to the area of Polygon C to find the area of Polygon D.\newlineThe area of Polygon C is 4040 square units. We multiply this by the scale factor squared to find the area of Polygon D.\newlineArea of Polygon D = Area of Polygon C ×\times (Scale factor squared)\newlineArea of Polygon D = 40×(14)40 \times (\frac{1}{4})
  4. Perform multiplication for area: Perform the multiplication to find the area of Polygon D.\newlineArea of Polygon D = 40×1440 \times \frac{1}{4}\newlineArea of Polygon D = 404\frac{40}{4}\newlineArea of Polygon D = 1010

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