Response
It is indeed a marvelous example of how great was the Ancient Greek thought. The book in which the Heron's formula is found is dated back to 60 AD, however, the Wiki page suggests that this formula was known by Archimedes, who lived two centuries before the book was published. The Mathisfun site offers a succinct explanation and history of the formula and also an interactive model where values for the triangle sides can be entered, and the triangle's area and angles will be automatically calculated. The angles, however, are found using the Law of Cosines and no proof of the Heron's Law is found on the page either. The Heron's formula is pretty much an achievement that is very easy to use to find triangle area.
Post 2:
Indeed, the Heron’s Law is extremely useful in finding the area of the triangles which are not right. The semiperimeter used in this formula is easy to calculate without any technical instruments. The calculations really get simplified when this formula is used. I suppose the people of the Ancient times relied on it in their calculations (used in agriculture or architecture I suppose). The only thing making these calculations complex is the square root which is rather hard to find without a calculator. Nevertheless, it is a much easier way since the classical way with height requires way more calculations involving square roots. Also, the formula provides knowledge of how do the perimeter and area of the triangle correspond which may be useful for general or mathematical purposes.
