Difference between revisions of "Heron's Formula"
(→External Links) |
StarWarsLiam (talk | contribs) m (Advertising lol) |
||
| Line 9: | Line 9: | ||
where the [[semi-perimeter]] <math>s=\frac{a+b+c}{2}</math>. | where the [[semi-perimeter]] <math>s=\frac{a+b+c}{2}</math>. | ||
| + | You can consider taking Introduction to Geometry for a detailed exposure! | ||
== Proof == | == Proof == | ||
Revision as of 12:09, 6 June 2012
Heron's Formula (sometimes called Hero's formula) is a formula for finding the area of a triangle given only the three side lengths.
Contents
Theorem
For any triangle with side lengths 
, the area 
can be found using the following formula:
where the semi-perimeter 
.
You can consider taking Introduction to Geometry for a detailed exposure!
Proof
![$[ABC]=\frac{ab}{2}\sin C$](http://latex.artofproblemsolving.com/a/c/4/ac4b71b27e69d9e101968239d56c96a437257a1d.png)
![$=\sqrt{\frac{a^2b^2}{4}\left[1-\frac{(a^2+b^2-c^2)^2}{4a^2b^2}\right]}$](http://latex.artofproblemsolving.com/6/d/1/6d165f658a8a212657a849e8c47d47d0700ce7aa.png)
See Also
External Links
In general, it is a good advice not to use Heron's formula in computer programs whenever we can avoid it. For example, whenever vertex coordinates are known, vector product is a much better alternative. Main reasons:
- Computing the square root is much slower than multiplication.
- For triangles with area close to zero Heron's formula computed using floating point variables suffers from precision problems.
