Answer:
512cm^2
Step-by-step explanation:
Let's imagine cutting the square down that diagonal. Now, we have two isosceles right triangles with a hypotenuse with length 32cm. Let's take one of those triangles for now and focus on it. Let's give the one of the legs of a triangle some length x. Since both legs are the same length, by the Pythagorean theorem:
[tex]x^2+x^2=32^2\\\\2x^2=1024\\\\x^2=512\\\\x=\sqrt{512}[/tex]
Since this leg makes up one side of the square, we can use it to calculate the area of the square, which is just the side length squared:
[tex]A=(\sqrt{512})^2 = 512[/tex]
