Segment of an Ellipse

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • ellipse segment 3hollow ellipse s major s minor 3Ellipse 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.

 

Ellipse Segment Area formula

\(\large{ A_{area} = \frac{c\;d}{4} \;  \left[ arccos \left( 1-\frac{2\;h}{c} \right) - \left( 1-\frac{2\;h}{c} \right) \; \sqrt{ \frac{4\;h}{c} } - \frac{4\;h^2}{c^2}     \right]    }\)   

Where:

 Units English Metric
\(\large{ A_{area} }\) = area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ h }\) = height \(\large{ in }\) \(\large{ mm }\)
\(\large{ c }\) = major axis \(\large{ in }\) \(\large{ mm }\)
\(\large{ d }\) = minor axis \(\large{ in }\) \(\large{ mm }\)

 

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