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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 $Y$ 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 $Z$ . $\newline$ What is the area of Polygon $Z$ ? $\newline$ square units

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Scale drawings: word problems

Full solution

Q. 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

.

\newline

What is the area of Polygon

Z

?

\newline

square units

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). $\newline$ Area of Polygon Y: $11$ square units. Scale factor: $3$ .
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.
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. $\newline$ Area of Polygon Z = $(\text{Scale factor})^2 \times \text{Area of Polygon Y} = 3^2 \times 11 = 9 \times 11$ .
Perform Multiplication: Perform the multiplication to find the area of Polygon Z. $\newline$ Area of Polygon Z = $9 \times 11 = 99$ square units.

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