Definition:Altitude of Geometric Figure
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
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
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
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
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
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): altitude: 1.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): altitude: 1.