Parabolic Segment and Spandrel

Area and Centroid

A parabola is the locus (position) of points in that plane that are equidistant from both the directrix and the focus.

Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface

The focus of a parabola at distance a from its vertex and is given by:

The area of parabolic segment is:

The location of the centroid from the base is:

Semiparabola and spandrel of parabola

For semiparabolic segment:

For spandrel of parabola:

General spandrel

For the general spandrel shown:

The moment of inertia about the x- and y-axes is:

Length of parabolic arc

In general, the length of a parabolic arc from point 1 to point 2 is:

The total length of the parabolic arc shown may be calculated by: