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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 ?
square units

Polygon $C$ has an area of $40$ square units. Kennan drew a scaled version of Polygon $C$ using a scale factor of $\frac{1}{2}$ and labeled it Polygon $D$ . $\newline$ What is the area of Polygon $D$ ? $\newline$ square units

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Scale drawings: word problems

Full solution

Q. Polygon

C

has an area of

40

square units. Kennan drew a scaled version of Polygon

C

using a scale factor of

\frac{1}{2}

and labeled it Polygon

D

.

\newline

What is the area of Polygon

D

?

\newline

square units

Understand relationship scale factor: Understand the relationship between the scale factor and the area of similar polygons. $\newline$ When a polygon is scaled by a factor of $k$ , the area of the polygon is scaled by a factor of $k^2$ . This is because area is a two-dimensional measurement, and scaling affects both dimensions (length and width).
Calculate scale factor squared: Calculate the scale factor squared. Since the scale factor is $\frac{1}{2}$ , we square it to find the factor by which the area will be scaled. $\left(\frac{1}{2}\right)^2 = \frac{1}{4}$
Apply scale factor to area: Apply the scale factor squared to the area of Polygon C to find the area of Polygon D. $\newline$ The area of Polygon C is $40$ square units. We multiply this by the scale factor squared to find the area of Polygon D. $\newline$ Area of Polygon D = Area of Polygon C $\times$ (Scale factor squared) $\newline$ Area of Polygon D = $40 \times (\frac{1}{4})$
Perform multiplication for area: Perform the multiplication to find the area of Polygon D. $\newline$ Area of Polygon D = $40 \times \frac{1}{4}$ $\newline$ Area of Polygon D = $\frac{40}{4}$ $\newline$ Area of Polygon D = $10$

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