Answer:
1/4
Step-by-step explanation:
The scale factor is \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction, so each side length of the polygon was multiplied by \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction.
Hint #22 / 4
Key idea
If the length of a figure scales by xxx, then area of the figure scales by x^2x
2
x, squared.
The Polygon QQQ is created with a scale factor of \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction. So, the area of Polygon QQQ scales by \left({\dfrac12}\right)^2(
2
1
)
2
left parenthesis, start fraction, 1, divided by, 2, end fraction, right parenthesis, squared.
[Show me why this works.]
PP
llww
P=lwP, equals, l, w
QQQQ\dfrac12
start fraction, 1, divided by, 2, end fractionPP\dfrac12
start fraction, 1, divided by, 2, end fraction
\begin{aligned} A &= \left(l\times\dfrac12\right)\times\left(w\times\dfrac12\right) \\ \\ A&= l\times w\times\dfrac12\times\dfrac12 \\ \\ A&= lw \times \left({\dfrac12}\right)^2\\ \\ A&= lw \times {\dfrac1{4}} \end{aligned}
Q=lw\times\dfrac1{4}
Q, equals, l, w, times, start fraction, 1, divided by, 4, end fraction
PPQQ
P=lwP, equals, l, w
Q=lw\times\dfrac1{4}
Q, equals, l, w, times, start fraction, 1, divided by, 4, end fraction
Hint #33 / 4
\left({\dfrac12}\right)^2= {\dfrac12\times\dfrac12}=\dfrac1{4}(
2
1
)
2
=
2
1
×
2
1
=
4
1
left parenthesis, start fraction, 1, divided by, 2, end fraction, right parenthesis, squared, equals, start fraction, 1, divided by, 2, end fraction, times, start fraction, 1, divided by, 2, end fraction, equals, start fraction, 1, divided by, 4, end fraction
Hint #44 / 4
Polygon QQQ is \dfrac1{4}
4
1
start fraction, 1, divided by, 4, end fraction the size of Polygon PPP.
) to solve for the area.