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. altitudeMathworldPlanetmath), 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 h1 and h2 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 parallelogramMathworldPlanetmath 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 triangleMathworldPlanetmath, 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