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 with explanation:

→It is given  that Polygon Y is scaled copy of polygon X ,with a scale factor of

$\frac{1}{3}$.

→Pre -image =Polygon X

→Image =Polygon Y

→Scale factor $=\frac{1}{3}$

→When polygon is dilated by scale factor greater than 1 or less than 1, the two polygons, that is image and Pre-image are similar to each other.

→In this problem , Scale factor <1.

→So, Polygon Y ,shape will be Smaller than ,Polygon X.

→As,sides of two polygon will be proportional to each other,So, Sides of Polygon Y will be $=\frac{1}{3}$ of polygon X.

→If Area of polygon X is A, then Area of Polygon Y will be , $=\frac{A}{3}$

$\frac{\text{Area of polygon X}}{\text{Area of Polygon Y}}=\frac{3}{1}=3\\\\{\text{Or}}\\\\\frac{\text{Area of polygon Y}}{\text{Area of Polygon X}}=\frac{1}{3}$