Answer
$A=\displaystyle \frac{1}{2}x^{2}$
Work Step by Step
The only two sides that can be equal are the legs of the right triangle.
(The hypotenuse is longer than any of the legs)
The area is $\displaystyle \frac{1}{2}\cdot$(leg)(leg)
With $x$ representing the length of the legs, the function for the area is:
$A(x)=\displaystyle \frac{1}{2}\cdot x\cdot x$
$A=\displaystyle \frac{1}{2}x^{2}$