Polygon D is a scaled copy of Polygon C using a scale factor of 6 . How many times as large is the area of Polygon D compared to the area Polygon C ?

Denote Area of Polygons: Let's denote the area of Polygon C as A_C and the area of Polygon D as A_D. 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 6, we can write the relationship between their areas as A_D = (scale factor)^2 * A_C.Calculate Scale Factor: The scale factor given is 6. To find out how many times larger the area of Polygon D is compared to Polygon C, we need to square the scale factor: (6)^2 = 36.Compare Areas: Therefore, the area of Polygon D is 36 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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Polygon
D is a scaled copy of Polygon
C using a scale factor of 6 .
How many times as large is the area of Polygon
D compared to the area Polygon
C ?

Polygon $D$ is a scaled copy of Polygon $C$ using a scale factor of $6$ . $\newline$ How many times as large is the area of Polygon $D$ compared to the area Polygon $C$ ?

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Algebra 1

Area and perimeter: word problems

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Q. Polygon

D

is a scaled copy of Polygon

C

using a scale factor of

6

\newline

How many times as large is the area of Polygon

D

compared to the area Polygon

C

Denote Area of Polygons: Let's denote the area of Polygon C as $A_C$ and the area of Polygon D as $A_D$ . 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 $6$ , we can write the relationship between their areas as $A_D = (\text{scale factor})^2 \times A_C$ .
Calculate Scale Factor: The scale factor given is $6$ . To find out how many times larger the area of Polygon D is compared to Polygon C, we need to square the scale factor: $(6)^2 = 36$ .
Compare Areas: Therefore, the area of Polygon D is $36$ 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.