Question

Polygon Y is a scaled copy of Polygon X using a scale factor of \dfrac13 3 1 ​ start fraction, 1, divided by, 3, end fraction. Polygon Y's area is what fraction of Polygon XXX's area?

Answer 1

Answer:

Polygon Y's area is one ninth (1/9) of Polygon X'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

In this problem

Let

z-----> the scale factor

a-----> Polygon Y's area

b----> Polygon X's area

$z^{2}=\frac{a}{b}$

we have

$z=\frac{1}{3}$

substitute

$(\frac{1}{3})^{2}=\frac{a}{b}$

$\frac{1}{9}=\frac{a}{b}$

$a=\frac{1}{9}b$

therefore

Polygon Y's area is one ninth (1/9) of Polygon X's area