Height (geometry, $h$)

A height is a distance measured perpendicular to a specified base or reference surface, or along a specified vertical direction. The reference and direction are part of the definition.

For a triangle, the height to a chosen side is the perpendicular distance from the opposite vertex to the line containing that side, giving area $A=bh/2$. For an inclined object, its length and vertical height differ. In a uniform gravitational field, a change in vertical height gives a gravitational potential-energy change $mg\Delta h$.