Segment of an Ellipse

Segment Area formula
$\large{ A_{area} \;=\; \dfrac{c\cdot d}{4} \; \left[ arccos \left( 1-\dfrac{2\cdot h}{c} \right) - \left( 1-\dfrac{2\cdot h}{c} \right) \cdot \sqrt{ \dfrac{4\cdot h}{c} } - \dfrac{4\cdot h^2}{c^2} \right] }$
Symbol	English	Metric
$A_{area}$ = area	$in^2$	$mm^2$
$h$ = height	$in$	$mm$
$c$ = major axis	$in$	$mm$
$d$ = minor axis	$in$	$mm$

Ellipse segment (a two-dimensional figure) is an interior part of an ellipse bound by a chord and an ellipse.
Chord is a line segment on the interior of the ellipse.
Major axis is always the longest axis in an ellipse.
Minor axis is always the shortest axis in an ellipse.
Semi-major axis is half of the longest axis of an ellipse.
Semi-minor axis is half of the shortest axis of an ellipse.