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A formula expressing the surface area <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/h/h047/h047120/h0471201.png" /> of a triangle in terms of its sides <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/h/h047/h047120/h0471202.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/h/h047/h047120/h0471203.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/h/h047/h047120/h0471204.png" />:
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A formula expressing the surface area $S$ of a triangle in terms of its sides $a$, $b$ and $c$:
  
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<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/h/h047/h047120/h0471205.png" /></td> </tr></table>
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$$S=\sqrt{p(p-a)(p-b)(p-c)},$$
  
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where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/h/h047/h047120/h0471206.png" />. Named after Heron (1st century A.D.).
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where $p=(a+b+c)/2$. Named after Heron (1st century A.D.).
  
  
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====References====
 
====References====
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<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  M. Berger,  "Geometry" , '''1–2''' , Springer  (1987)  (Translated from French)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  H.S.M. Coxeter,  "Introduction to geometry" , Wiley  (1961)</TD></TR></table>
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<table>
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  M. Berger,  "Geometry" , '''1–2''' , Springer  (1987)  (Translated from French) {{ZBL|1153.51001}}</TD></TR>
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<TR><TD valign="top">[a2]</TD> <TD valign="top">  H.S.M. Coxeter,  "Introduction to geometry" , Wiley  (1961) {{ZBL|0095.34502}}</TD></TR>
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</table>

Revision as of 16:53, 17 September 2017

A formula expressing the surface area $S$ of a triangle in terms of its sides $a$, $b$ and $c$:

$$S=\sqrt{p(p-a)(p-b)(p-c)},$$

where $p=(a+b+c)/2$. Named after Heron (1st century A.D.).


Comments

References

[a1] M. Berger, "Geometry" , 1–2 , Springer (1987) (Translated from French) Zbl 1153.51001
[a2] H.S.M. Coxeter, "Introduction to geometry" , Wiley (1961) Zbl 0095.34502
How to Cite This Entry:
Heron formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Heron_formula&oldid=14041
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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