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> | ||
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+ | ==Isosceles Triangle Simplification== | ||
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+ | <math>A=\sqrt{s(s-a)(s-b)(s-c)}</math> for all triangles | ||
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+ | <math>b=c</math> for all isosceles triangles | ||
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+ | <math>A=\sqrt{s(s-a)(s-b)(s-b)}</math> simplifies to <math>A=(s-b)\sqrt{s(s-a)}</math> <math>\blacksquare</math> | ||
==Example== | ==Example== |
Revision as of 17:18, 8 March 2017
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
Isosceles Triangle Simplification
for all triangles
for all isosceles triangles
simplifies to
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.