Difference between revisions of "Heron's Formula"
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<math>=\sqrt{s(s-a)(s-b)(s-c)}</math> | <math>=\sqrt{s(s-a)(s-b)(s-c)}</math> | ||
+ | ==Example== | ||
+ | Let's say that you have a right triangle with the sides 3,4, and 5. Your semi- perimeter would be 6. | ||
+ | Then you have 6-3=3, 6-4=2, 6-5=1. | ||
+ | 1+2+3= 6 | ||
+ | <math> 6*6 = 36</math> | ||
+ | The square root of 36 is 6. The area of your triangle is 6. | ||
== See Also == | == See Also == | ||
* [[Brahmagupta's formula]] | * [[Brahmagupta's formula]] |
Revision as of 16:52, 21 June 2016
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
[hide]Theorem
For any triangle with side lengths , the area can be found using the following formula:
where the semi-perimeter .
Proof
Example
Let's say that you have a right triangle with the sides 3,4, and 5. Your semi- perimeter would be 6. Then you have 6-3=3, 6-4=2, 6-5=1. 1+2+3= 6 The square root of 36 is 6. The area of your triangle is 6.
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.