1, triangle area formula in the form of two angles: Let the opposite sides of three angles A, B and C of triangle ABC be A, B and C respectively, and the area of triangle ABC be S, then (1) s = (1/2) absinc; (2)S =( 1/2)acsinB； (3)S=( 1/2)bcsinA .
2. The formula for calculating the triangle area by using the perimeter of the triangle and the radius of the inscribed circle: Let the opposite sides of the three angles A, B and C of the triangle ABC be A, B and C, the radius of the inscribed circle of the triangle is R, and the area of the triangle ABC is S, then S = (1/2) x (a+b+c) R. This area formula shows that the area of the triangle is equal to.
3. Helen Qin Jiushao formula: Let the opposite sides of the three angles A, B and C of the triangle ABC be A, B and C respectively, and the area of the triangle ABC is S, then S=√[p(p-a)(p-b)(p-c)]. Where "√" is the big root sign and "p" is the half circumference, that is, p=(a+b+c)/2.
Derivation method of triangle area formula;
4. Divide the triangle into two triangles with equal area, draw a vertical line from the vertex to the bottom of the triangle, and divide the triangle into two right-angled triangles.
This vertical line is the height of the triangle, which is perpendicular to the bottom and divides the bottom into two parts. Assuming that the length of the base is b and the length of the height is h, the area of the triangle is: area = length of the base × height ÷2=bh÷2.
Application of triangle area formula
1. In the field of mathematics, the triangle area formula can be used to calculate the triangle area. You only need to know the base and height of the triangle, and you can use the formula to calculate the area of the triangle.
2. The triangle area formula can also be applied to the fields of physics and engineering. For example, in mechanics, the triangle area formula can be used to calculate the length of the arm of force, so as to get the torque of the lever. In civil engineering, the triangular area formula can be used to calculate the cross-sectional area, so as to obtain the size and bearing capacity of structural members.
3. The triangle area formula can also be applied in the field of economics. For example, in finance, the triangle area formula can be used to calculate the risk and return of portfolio. In statistics, the triangle area formula can be used to calculate the confidence interval and error rate of samples.