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?

49

Step-by-step explanation:

Area of a rectangle is length, ll, times width, ww.

Area of Polygon V=lwV=lw

Now, we need to find the area of Polygon WW. Since Polygon WW was created with a scale factor of 77, we need to multiply each side length in Polygon VV by 77.

We need to multiply the new side lengths to find the new area:

\begin{aligned} A &= (l\times7)\times(w\times7) \\ \\ A&= l\times w\times7\times7 \\ \\ A&= lw \times {7}^2\\ \\ A&= lw \times {49} \end{aligned}

A

A

A

A

​

=(l×7)×(w×7)

=l×w×7×7

=lw×7

2

=lw×49

​

Area of Polygon W=lw\times49W=lw×49

Key idea

The area of a polygon created with a scale factor of xx is x^2x

2

times larger than the original polygon:

\text{scale factor}^2=\text{how many times larger area of scale copy is}scale factor

2

=how many times larger area of scale copy is

The area of Polygon WW is 4949 times the area of Polygon VV.

Area of Polygon V \times 49=V×49= Area of Polygon WW

1\times49=491×49=49

The area of Polygon WW is 4949 square units.

49 square units

Step-by-step explanation:

When the length of the sides of a figure are increased by a scale factor, the area is increased by the square of that scale factor.

Since the scale factor used is 7, this means the area is increased by a factor of 7² = 49.

Multiplying the area of polygon V by the scale factor, we have 1(49) = 49.

step-by-step explanation:

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