You can calculate triangle area when you know all three sides by using heron's formula. you can also use a formula discovered by the chinese which i found in wikipedia. the formula does work (but i don't know what they mean by a> =b> =c). my question is, does this formula have a name?

It is a rearrangement of Heron's formula

Step-by-step explanation:

Straightforward expansion of Heron's formula will result in a set of terms that can be arranged to the form of your second formula.

Interestingly, the trig formula for the area of a triangle can also be used to produce Heron's formula and/or your Chinese formula, using the Law of Cosines to relate side lengths to angle.

Area = (1/2)ab·sin(C)

cos(C) = (a^2+b^2-c^2)/(2ab)

sin(C) = √(1 -cos(C)^2)

The requirement to order a, b, c from longest to shortest should not be necessary. If the triangle inequality is met, the product under the radical in Heron's formula will always be positive. Since the other formula is simply a rearrangement of that, the same should be true there.

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