Question

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

Answer 1

Answer:

1/9

Step-by-step explanation:

(1/3)^2 = 1/3 x 1/3 =1/9

plus I checked the answer after I got it wrong so...

Answer 2

Answer:

$\frac{1}{9}$

Step-by-step explanation:

This is a case of enlargement of a figure of scale factor $\frac{1}{3}$.

In any enlargement, $Area(F')=k^2 Area(F)$, where the transformation maps F onto F'.

In this case, let F be polygon XXX and let F' be polygon YYY. Hence,

$Area(YYY) = k^2 Area (XXX)$

$Area(YYY) = (\frac{1}{3})^2 Area(XXX)$

$Area(YYY) = \frac{1}{9} Area(XXX)$

Therefore, the area of polygon YYY is $\frac{1}{9}$ of the area of polygon XXX.