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Polygon
V has an area of 1 square unit. Jun-seo drew a scaled version of Polygon
V using a scale factor of 7 and labeled it Polygon
W.
What is the area of Polygon
W ?
square units

Polygon $V$ has an area of $1$ square unit. Jun-seo drew a scaled version of Polygon $V$ using a scale factor of $7$ and labeled it Polygon $W$ . $\newline$ What is the area of Polygon $W$ ? $\newline$ square units

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Solve proportions: word problems

Full solution

Q. Polygon

V

has an area of

1

square unit. Jun-seo drew a scaled version of Polygon

V

using a scale factor of

7

and labeled it Polygon

W

.

\newline

What is the area of Polygon

W

?

\newline

square units

Identify Area and Scale Factor: Identify the original area of Polygon $V$ and the scale factor used to create Polygon $W$ .\ Polygon $V$ has an area of $1$ square unit. The scale factor used to create Polygon $W$ is $7$ .
Relationship Between Scale Factor and Area: Understand the relationship between the scale factor and the area of similar polygons. $\newline$ When a two-dimensional figure is scaled by a factor of 'k ext{', the area of the resulting figure is '} ext{k}^\(2 ext{'} times the area of the original figure.
Calculate Area of Polygon W: Calculate the area of Polygon W using the scale factor. $\newline$ Since the scale factor is $7$ , we square it to find the area of Polygon W: Area of Polygon W = (Scale factor) $^2$ * Area of Polygon V = $7^2$ * $1$ = $49$ square units.

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