The triangle area formula is (area = bottom × height ÷2. Where A is the base of the triangle and H is the height corresponding to the base) Note: All three sides can be the base, which should be understood as: half of the product of the heights corresponding to the three sides is the area of the triangle. This is the basis of finding the length of line segment by area method.

The area formula of a regular triangle is (where a is the side length of the triangle).

Let three sides of the triangle be AC, BC and AB, and point D is perpendicular to AB, which is the height of the triangle ABC. Cosb can be expressed by cosine theorem.

Using cosine theorem: then using Pythagorean theorem, we get the reuse area of CD = bottom × height ÷2, and finally get the area formula.

Extended data:

In the plane rectangular coordinate system, the area of the triangle composed of A(a, b), B(c, d) and C(e, f) is

. A, B and C are best taken in counterclockwise order from the upper right corner, because the results obtained in this way are generally positive. If you don't follow this rule, you may get a negative value, just taking an absolute value, which will not affect the size of the triangle area.

References:

Baidu encyclopedia-triangle