Difference between revisions of "Heron's Formula"
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== Proof 2 == | == Proof 2 == | ||
− | + | Imagine a triangle with an altitude dropped from vertex A. | |
− | + | Now the side of "a" is split into two sections. | |
+ | Label the right section "x" and the left section "a-x". | ||
+ | Now we can prove Heron's formula. | ||
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<math>[ABC] = \frac{1}{2} * a * h</math> | <math>[ABC] = \frac{1}{2} * a * h</math> | ||
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<math>[ABC] = \sqrt(s(s - a)(s - b)(s - c))</math> | <math>[ABC] = \sqrt(s(s - a)(s - b)(s - c))</math> |
Revision as of 19:08, 8 February 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
Proof 2
Imagine a triangle with an altitude dropped from vertex A. Now the side of "a" is split into two sections. Label the right section "x" and the left section "a-x". Now we can prove Heron's formula.
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.