Editing Heron's formula (section)

{{Short description|Triangle area in terms of side lengths}}
{{about|calculating the area of a triangle|calculating a square root|Heron's method}}
[[File:Triangle with notations 2 without points.svg|thumb|198px|A triangle with sides ''a'', ''b'', and ''c'']]
In [[geometry]], '''Heron's formula''' (or '''Hero's formula''') gives the [[area of a triangle]] in terms of the three side lengths {{tmath|a,}} {{tmath|b,}} {{tmath|c.}} Letting {{tmath|s}} be the [[semiperimeter]] of the triangle, <math>s = \tfrac12(a + b + c),</math> the area {{tmath|A}} is<ref>{{cite journal
 | last = Kendig
 | first = Keith
 | doi = 10.1080/00029890.2000.12005213
 | issue = 5
 | journal = [[The American Mathematical Monthly]]
 | jstor = 2695295
 | mr = 1763392
 | pages = 402–415
 | title = Is a 2000-year-old formula still keeping some secrets?
 | url = https://www.maa.org/programs/maa-awards/writing-awards/is-a-2000-year-old-formula-still-keeping-some-secrets
 | volume = 107
 | year = 2000
 | s2cid = 1214184
 | access-date = 2021-12-27
 | archive-date = 2024-05-29
 | archive-url = https://web.archive.org/web/20240529215533/https://maa.org/programs/maa-awards/writing-awards/is-a-2000-year-old-formula-still-keeping-some-secrets
 | url-status = dead
 }}</ref>

<math display=block>A = \sqrt{s(s-a)(s-b)(s-c)}.</math>

It is named after first-century engineer [[Heron of Alexandria]] (or Hero) who proved it in his work ''Metrica'', though it was probably known centuries earlier.