Let
b------> the length side of a square
we know that
the area of a square is equal to
[tex]A=b^{2}[/tex]
Find the length side of the diagonal applying the Pythagoras Theorem
[tex]d^{2}=b^{2}+b^{2}[/tex]
[tex]d^{2}=2b^{2}[/tex]
[tex]d=b\sqrt{2}\ units[/tex]
Remember that
[tex]d=x\ units[/tex] -----> given problem
substitute
[tex]d=b\sqrt{2}\ units[/tex]
[tex]x=b\sqrt{2}\ units[/tex]
Solve for b
[tex]b=\frac{x\sqrt{2}}{2}\ units[/tex]
Substitute in the formula of area
[tex]A=(\frac{x\sqrt{2}}{2})^{2}[/tex]
[tex]A=\frac{x^{2}}{2}\ units^{2}[/tex]
therefore
the answer is
[tex]\frac{x^{2}}{2}\ units^{2}[/tex]
