Definition:Altitude of Geometric Figure

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Definition

The altitude of a geometric figure $\FF$ is the length of a line segment giving the height of $\FF$.


Altitude of Polygon

An altitude of a polygon is the longest perpendicular from the base to a vertex most distant from the base.


Altitude of Polyhedron

An altitude of a polyhedron is the longest perpendicular from the base to a vertex most distant from the base.


Altitude of Cone

HeightOfCone.png

Let a perpendicular $AE$ be dropped from the apex of a cone to the plane containing its base.

The line segment $AE$ is an altitude of the cone.


Altitude of Cylinder

Cylinder.png


An altitude of a cylinder is a line segment drawn perpendicular to the base and its opposite plane.


In the above diagram, $HJ$ is an altitude of the cylinder $ACBDFE$.


Altitude of Prism

Prism.png

An altitude of a prism is a line which is perpendicular to the bases of the prism.

In the above diagram, a line of length $h$ is an altitude of the prism $AJ$.


Altitude of Pyramid

Pyramid.png

An altitude of a pyramid is a straight line perpendicular to the plane of the base to its apex.

In the above diagram, an altitude is a straight line length is $h$.


Also defined as

The word altitude is often used in the context of a geometric figure to mean the height.

However, on $\mathsf{Pr} \infty \mathsf{fWiki}$ it is preferred if the terms altitude and height are used specifically to mean respectively the perpendicular and its length, to avoid confusion.


Also see

  • Results about altitudes in the context of geometry can be found here.


Sources