【Haichuan Teahouse】Brain-teasing Series: Given the three sides of a triangle, find its area
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This post was last edited by Desert Fish on 2021-11-1 15:16. Given the three sides of a triangle, find its area. If it’s a right triangle, you can simply multiply the base by the height. But the three sides of this triangle are not Pythagorean numbers. How to find it?
Then, it is possible to make the height on one of the sides, divide it into two right triangles, and use the Pythagorean theorem along with equations to determine this height.
I tried to look for answers online; it doesn’t seem like there’s any more convenient way, does it?
If you use CAD to draw it directly and then calculate the area, that’s the fastest way
Still the same question: can CAD be used in middle school exams?
It seems that this formula was mentioned in the original discussion – what an expert! ! !
Helen’s formula for the area of a triangle is also known as the Heron formula, the Helen’s formula, the Hero’s formula, or the Helen–Qin Jiushao formula. It is a formula that uses the lengths of the three sides of a triangle to directly calculate its area. The expression is: S=√p(p-a)(p-b)(p-c); it features a neat form that makes it easy to remember. It is said that this formula was first derived by the ancient Greek mathematician Archimedes, and since it first appeared in Helen’s work \"Geometria\", it is known as Helen’s formula. Qin Jiushao of China also derived a similar formula, calling it the triclinic integration method.
If this formula was covered in middle school courses, of course it can be used directly. For those students who have not yet learned the formula, it is rather difficult for them to derive it on their own; they still need to use the Pythagorean theorem.
Haha, actually I can’t remember either. I think I mentioned this formula back in middle school. It’s been over 20 years since I graduated. Lately I’ve become quite interested in geometry, so I’m looking into it again
The Pythagorean theorem is fine, but the key equation here is extremely difficult to solve