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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 ?

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 ?

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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 ?
  1. Identify Area and Scale Factor: Identify the original area of Polygon C and the scale factor used to create Polygon D.\newlinePolygon C has an area of 4040 square units. The scale factor for Polygon D is 12\frac{1}{2}.
  2. Relationship with Area: Understand the relationship between the scale factor and the area of similar polygons. When a scale factor is applied to the dimensions of a shape, the area of the shape is scaled by the square of the scale factor k2k^2.
  3. Calculate Area of Polygon D: Calculate the area of Polygon D using the scale factor.\newlineSince the scale factor is 12\frac{1}{2}, the area of Polygon D will be (12)2(\frac{1}{2})^2 times the area of Polygon C. Therefore, the area of Polygon D is (12)2×40(\frac{1}{2})^2 \times 40 square units.
  4. Perform Calculation: Perform the calculation to find the area of Polygon D.\newlineArea of Polygon D = (12)2×40=(14)×40=10(\frac{1}{2})^2 \times 40 = (\frac{1}{4}) \times 40 = 10 square units.

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