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Polygon 
Y has an area of 11 square units. Celia drew a scaled version of Polygon 
Y using a scale factor of 3 and labeled it Polygon 
Z.
What is the area of Polygon 
Z ?
square units

Polygon Y Y has an area of 1111 square units. Celia drew a scaled version of Polygon Y Y using a scale factor of 33 and labeled it Polygon Z Z .\newlineWhat is the area of Polygon Z Z ?\newlinesquare units

Full solution

Q. Polygon Y Y has an area of 1111 square units. Celia drew a scaled version of Polygon Y Y using a scale factor of 33 and labeled it Polygon Z Z .\newlineWhat is the area of Polygon Z Z ?\newlinesquare units
  1. Identify Area and Scale Factor: Identify the area of the original polygon (Polygon Y) and the scale factor used to create the scaled version (Polygon Z).\newlineArea of Polygon Y: 1111 square units. Scale factor: 33.
  2. Relationship Between Scale Factor and 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 is scaled by the square of the scale factor.
  3. Calculate Area of Polygon Z: Calculate the area of Polygon Z by squaring the scale factor and multiplying it by the area of Polygon Y.\newlineArea of Polygon Z = (Scale factor)2×Area of Polygon Y=32×11=9×11(\text{Scale factor})^2 \times \text{Area of Polygon Y} = 3^2 \times 11 = 9 \times 11.
  4. Perform Multiplication: Perform the multiplication to find the area of Polygon Z.\newlineArea of Polygon Z = 9×11=999 \times 11 = 99 square units.

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