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
`(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
`(5)/(6)`.

So,
`k=(5)/(6)`.

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

`k^2=\left((5)/(6)\right)^2`.

`k^2=(5^2)/(6^2)`

`k^2=(25)/(36)`

Therefore, the area of the figure will change by the factor of
`(25)/(36)`.