I'm given a hyperbolic segment, similar to the parabolic segment shown here: http://mathworld.wolfram.com/ParabolicSegment.html
I know the height of the segment ("h" in the wolfram article), and the length of the line segment joining the endpoints of the hyperbola ("2a" in the wolfram article).
Is it possible to find the area of the segment? Also, does there exist an approximation formula, or rapidly converging method to determine the approximate arc length of the given hyperbola?