Question

Polygon q is a scaled copy of polygon p using a scale factor of 1/2 polygon q’s area is what fraction of polygon p’s area?

Answer 1

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.

Answer 2

Answer:

Polygon q’s area is one fourth of polygon p’s area

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale factor

x-----> polygon q’s area

y-----> polygon p’s area

so

$z^{2} =\frac{x}{y}$

In this problem we have

$z=\frac{1}{2}$

substitute

$(\frac{1}{2})^{2} =\frac{x}{y}$

$(\frac{1}{4}) =\frac{x}{y}$

$x=\frac{1}{4}y$

therefore

Polygon q’s area is one fourth of polygon p’s area