1, Helen's formula: √p×(p-a)×(p-b)×(p-c): Helen's formula is one of the advanced methods to calculate the area of a triangle, which is suitable for the situation that the lengths of three sides of a triangle are known. P represents the half circumference, that is, (a+b+c)/2, and a, b and c represent the lengths of three sides of a triangle respectively. This formula does not need to know the height line of a triangle, but only needs the length of three sides to calculate the area.

2. Using the radius of the inscribed circle of the triangle: r×(a+b+c)/3: When the three bisectors of the triangle are equal to the radius of the circumscribed circle, the area can be calculated by using the radius of the inscribed circle of the triangle. Where R represents the radius of the inscribed circle, and A, B and C represent the lengths of the three sides of the triangle respectively. This formula is suitable for solving right-angled triangles and triangles in some special cases.

3. Using the radius of the circumscribed circle of the triangle: R×sin(A)×b/2: When the three sides of the triangle are equal, the area can be calculated by using the radius of the circumscribed circle of the triangle and the sine theorem. R represents the radius of the circumscribed circle, A represents the degree of angle A, and B represents the length of the base of the triangle. This formula is suitable for solving equilateral triangles and triangles in some special cases.

The importance of triangle

1, a triangle is the simplest polygon. It consists of three sides, each of which is connected by a point. The sum of three angles of a triangle is equal to 180 degrees, which is an important property of a triangle. This property can be used to prove many geometric theorems and solve many geometric problems.

2. Triangle is widely used in geometry. For example, triangles are very useful tools in measuring land and calculating area and volume. In engineering, triangles are often used to design structures because of their stability and robustness.

3. Triangle is also related to many important mathematical concepts. For example, trigonometric function is the functional relationship between the sides and angles of a triangle, which is widely used in solving geometric problems, numerical calculation and signal processing. In addition, triangles are related to concepts such as matrix and vector, and are widely used in scientific calculation, computer graphics and other fields.