Let's suppose that the dashed line bisect the right angle and the figure is a square. Then, we can draw the following picture
then, we can draw the following right triangle
and we need to find x. This can be done as

then x is equal to

since cos 45 is
![\cos 45=\frac{1}{\sqrt[]{2}}](https://img.qammunity.org/2023/formulas/mathematics/college/8cnx7qildfe2tkojffnf2p5t2l2lld7enb.png)
then, x is given by
![x=\frac{8}{\sqrt[]{2}}](https://img.qammunity.org/2023/formulas/mathematics/college/9n1v0g14oznpvydhxepsvtc8dwpv2nv4aw.png)
We can note that the length of one side of our square is

so, the one side is equal to
![\begin{gathered} L=2*\frac{8}{\sqrt[]{2}} \\ L=8\sqrt[]{2} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/jauv32tbbjq0x0ljahu7jx9vrpauibm6vq.png)
Since the area of a square is

the area of our figure is equal to
![\begin{gathered} A=(8\sqrt[]{2})^2 \\ A=64*2 \\ A=128 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/s0xfhdagvriq4zap8j03llfjziw85ctp36.png)
That is, the area of the square is equal to 128 centimeters squared.