Maximum Area of a Triangle on a Parabola

One of the vertices of a triangle lies on the line $y=9$. The two other vertices, whose $y$-coordinates are both less than $9$, are on the parabola $y=x^2$, and the side of the triangle with these two vertices as endpoints is parallel to the $x$-axis. What is the maximum possible area of the triangle? The answer is in the form $\sqrt{m}$ where $m$ is a positive integer. Input the value of $m$.