base and height of triangle

Considering the area of a triangle, one usually names a side of the triangle to be its base.  For expressing the calculation way of the area of the triangle, one then uses the height (a.k.a. altitude), which means the perpendicular distance of the vertex, to the base side, from the line determined by the base.  In the above two triangles, the heights $h_1$ and $h_2$ correspond the horizontal . One calls foot of the height the projection of the vertex onto the line of the base.

The rule for the calculation reads

area  =  base times height divided by 2

In the below figure, there is the illustration of the rule.  The parallelogram $ABCD$ has been divided by the diagonal $BD$ into two triangles, which are congruent by the ASA criterion (see the alternate interior angles).  Thus the both triangles have the areas half of the area of the parallelogram, which in turn has the common base $AB$ and the common height $h$ with the triangle $ABD$.

Note.  In an isosceles triangle, one sometimes calls the two equal sides the legs and the third side the base.

Title	base and height of triangle
Canonical name	BaseAndHeightOfTriangle
Date of creation	2013-03-22 18:50:15
Last modified on	2013-03-22 18:50:15
Owner	pahio (2872)
Last modified by	pahio (2872)
Numerical id	14
Author	pahio (2872)
Entry type	Definition
Classification	msc 51M25
Classification	msc 51M04
Classification	msc 51-01
Synonym	base of triangle
Synonym	height of triangle
Related topic	AreaOfAPolygonalRegion
Related topic	HeightOfATriangle
Related topic	Area2
Related topic	ProjectionFormula
Related topic	OrthicTriangle
Defines	base
Defines	height
Defines	foot of height
Defines	foot of altitude