Question

If a figure is dilated by a factor of 5/6 Area of a figure will change by a factor of

Answer 1

Given:

A figure is dilated by a factor of $\dfrac{5}{6}$.

To find:

The factor by which the area of the figure will change.

Solution:

We know that, if a figure is dilated by a factor k then the area of that figure is change by a factor of k² .

A figure is dilated by a factor of $\dfrac{5}{6}$.

So, $k=\dfrac{5}{6}$.

The area of the figure will change by a factor of k² .

$k^2=\left(\dfrac{5}{6}\right)^2$.

$k^2=\dfrac{5^2}{6^2}$

$k^2=\dfrac{25}{36}$

Therefore, the area of the figure will change by the factor of $\dfrac{25}{36}$.