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$Polygon Q is a scaled copy of Polygon P using a scale factor of (1)/(2). Polygon Q 's area is what fraction of Polygon P^(') 's area?$

Polygon $Q$ is a scaled copy of Polygon $P$ using a scale factor of $\frac{1}{2}$ . $\newline$ Polygon $Q$ 's area is what fraction of Polygon $P^{\prime} \mathrm{s}$ area?

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Scale drawings: word problems

Full solution

Q. Polygon

Q

is a scaled copy of Polygon

P

using a scale factor of

\frac{1}{2}

.

\newline

Polygon

Q

's area is what fraction of Polygon

P^{\prime} \mathrm{s}

area?

Identify Relationship: Identify the relationship between the scale factor and the area of similar polygons. When a polygon is scaled by a factor of $k$ , the area is scaled by a factor of $k^2$ . In this case, the scale factor is $\frac{1}{2}$ .
Calculate Scale Factor: Calculate the area scale factor by squaring the linear scale factor. The linear scale factor is $\frac{1}{2}$ , so the area scale factor is $(\frac{1}{2})^2$ .
Perform Calculation: Perform the calculation for the area scale factor. $(\frac{1}{2})^2 = \frac{1}{4}$ . This means that the area of Polygon $Q$ is $\frac{1}{4}$ the area of Polygon $P$ .

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