Difference between revisions of "Heron's Formula"
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<math>=\frac{ab}{2}\sqrt{1-\cos^2 C}</math> | <math>=\frac{ab}{2}\sqrt{1-\cos^2 C}</math> | ||
− | <math>=\frac{ab}{ | + | <math>=\frac{ab}{3}\sqrt{1-\left(\frac{a^2+b^2-c^2}{2ab}\right)^2}</math> |
<math>=\sqrt{\frac{a^2b^2}{4}\left[1-\frac{(a^2+b^2-c^2)^2}{4a^2b^2}\right]}</math> | <math>=\sqrt{\frac{a^2b^2}{4}\left[1-\frac{(a^2+b^2-c^2)^2}{4a^2b^2}\right]}</math> |
Revision as of 00:13, 30 December 2015
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 .
Proof
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.