Answer:
1/3
Step-by-step explanation:
The area of Polygon GGG is \dfrac19
9
1
start fraction, 1, divided by, 9, end fraction the area of Polygon FFF.
Each side of Polygon FFF was multiplied by a certain value, known as the scale factor , to result in an area that is \dfrac19
9
1
start fraction, 1, divided by, 9, end fraction the area of Polygon FFF.
[Show me an example of how scale factor affects area]
\dfrac1{10}
start fraction, 1, divided by, 10, end fraction
\begin{aligned} A &= \left(l\times\dfrac1{10}\right)\times\left(w\times\dfrac1{10}\right) \\ \\ A&= l\times w\times\dfrac1{10}\times\dfrac1{10} \\ \\ A&= lw \times \left(\dfrac1{10}\right)^2\end{aligned}
\dfrac1{10}
start fraction, 1, divided by, 10, end fraction\left(\dfrac1{10}\right)^2
left parenthesis, start fraction, 1, divided by, 10, end fraction, right parenthesis, start superscript, 2, end superscript
Hint #22 / 3
The area of a polygon created with a scale factor of \dfrac1x
x
1
start fraction, 1, divided by, x, end fraction has \left(\dfrac1{x}\right)^2(
x
1
)
2
left parenthesis, start fraction, 1, divided by, x, end fraction, right parenthesis, start superscript, 2, end superscript the area of the original polygon:
\left(\text{scale factor}\right)^2=\text{fraction of the area the scale copy has}(scale factor)
2
=fraction of the area the scale copy hasleft parenthesis, s, c, a, l, e, space, f, a, c, t, o, r, right parenthesis, start superscript, 2, end superscript, equals, f, r, a, c, t, i, o, n, space, o, f, space, t, h, e, space, a, r, e, a, space, t, h, e, space, s, c, a, l, e, space, c, o, p, y, space, h, a, s
The area of Polygon GGG is \dfrac19
9
1
start fraction, 1, divided by, 9, end fraction the area of Polygon FFF. Let's substitute \dfrac19
9
1
start fraction, 1, divided by, 9, end fraction into the equation to find the scale factor.
\left(\dfrac1{?}\right)^2=\dfrac19(
?
1
)
2
=
9
1
left parenthesis, start fraction, 1, divided by, question mark, end fraction, right parenthesis, start superscript, 2, end superscript, equals, start fraction, 1, divided by, 9, end fraction
The scale factor is \dfrac13
3
1
start fraction, 1, divided by, 3, end fraction.
Hint #33 / 3
Aimar used a scale factor of \dfrac13
3
1
start fraction, 1, divided by, 3, end fraction to go from Polygon FFF to Polygon GGG.
