Answer:
5 parts are shaded and 4 parts are white so:
There are 9 parts all together.
We can then form ratio's of the white areas and the shaded areas:
White Area Ratio =
[tex] \frac{4}{9} [/tex]
Shaded Area Ratio =
[tex] \frac{5}{9} [/tex]
Let the area of sqaure be equated to x, which means let the entire area of the square equal to x:
x = Area of whole square
Now we can form an equation :
[tex] \frac{5}{9} x = 165[/tex]
So now we just need to solve for x:
[tex]x = \frac{165}{ \frac{5}{9} } [/tex]
[tex]x = 297[/tex]
The area of the square is:
[tex]297 {cm}^{2} [/tex]
