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[parent] base and height of triangle (Definition)

\begin{pspicture}(-5,-0.5)(5,2.8) \rput(-5,-0.5){.} \rput(5,2.8){.} \pspolygon(-... ...yle=dashed](1,0)(2,0) \rput(3,-0.3){base} \rput(0.75,0.9){$h_2$} \end{pspicture}

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, which means the perpendicular distance of the vertex, opposite 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 bases.

The rule for the calculation reads $$\mbox{area \;=\; base times height divided by 2}$$

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 $ABD$ .


\begin{pspicture}(-3,-0.5)(4.5,2.8) \rput(-3,-0.5){.} \rput(4.5,2.8){.} \psline[... ...\psline[linestyle=dotted](-0.5,2.3)(-0.5,0) \rput(-0.3,1.1){$h$} \end{pspicture}

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




"base and height of triangle" is owned by pahio.
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See Also: area of a polygonal region, height, area, projection formula

Other names:  base of triangle, height of triangle
Also defines:  base, height
Keywords:  triangle

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Cross-references: legs, isosceles triangle, alternate interior angles, ASA, congruent, diagonal, parallelogram, line, vertex, distance, perpendicular, area, triangle, side, area of a triangle
There are 34 references to this entry.

This is version 8 of base and height of triangle, born on 2009-02-21, modified 2009-02-25.
Object id is 11642, canonical name is BaseAndHeightOfTriangle.
Accessed 3236 times total.

Classification:
AMS MSC51-01 (Geometry :: Instructional exposition )
 51M04 (Geometry :: Real and complex geometry :: Elementary problems in Euclidean geometries)
 51M25 (Geometry :: Real and complex geometry :: Length, area and volume)

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