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 =
![(4)/(9)](https://img.qammunity.org/2022/formulas/mathematics/college/i5jvu4zxwae5ojdzcovg2u5xas6uo8jul6.png)
Shaded Area Ratio =
![(5)/(9)](https://img.qammunity.org/2022/formulas/mathematics/high-school/uqf74hkxp1wc0t2anwabsmjn3i4gkqg6.png)
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 :
![(5)/(9) x = 165](https://img.qammunity.org/2022/formulas/mathematics/high-school/2xnfyu8mq1ietmzi55kmlgi3q8cq4ko05w.png)
So now we just need to solve for x:
![x = (165)/( (5)/(9) )](https://img.qammunity.org/2022/formulas/mathematics/high-school/rek0tkgoe8f7prqii1gam1iqmfkpcg6bqn.png)
![x = 297](https://img.qammunity.org/2022/formulas/mathematics/high-school/4chuqdsordire36wxd5wfm9nxilsr13mce.png)
The area of the square is:
![297 {cm}^(2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/5w3jy3cqhxd5dmaw7efijcz7hof0i7kxp9.png)