There are many methods to calculate the triangle area, the most common ones are parallelogram division and Helen formula. The following are detailed steps and knowledge expansion.

Method 1: parallelogram segmentation method

Suppose there is a parallelogram, we can divide it into two triangles.

The areas of these two triangles are S 1 and S2, respectively.

The area of the parallelogram is S=S 1+S2.

Therefore, the area of triangle S 1 or S2 can be expressed as S× 1/2. That is, S= 1/2× bottom× height.

Expand knowledge:

The application scope of parallelogram segmentation method is applicable to all types of triangles, whether right triangle, acute triangle or obtuse triangle. However, it should be noted that the bottom and the height must correspond, that is, the bottom is the side length corresponding to the height.

Method 2: Helen formula

Suppose the three sides of a triangle are A, B and C respectively, and the semi-circumference of the triangle is p=(a+b+c)/2.

Using the semi-perimeter p and Helen's formula S=sqrt(p*(p-a)*(p-b)*(p-c)), the area of the triangle can be obtained.

Expand knowledge:

Helen's formula is applicable to all types of triangles, but it should be noted that three sides of the triangle are needed in the calculation process, so it is necessary to determine the three sides first.

Helen formula can be derived, and the same area formula can be obtained by calculating the height and bottom length of triangle and then dividing by parallelogram.

Helen's formula plays an important role in mathematics. It is not only suitable for calculating the area of triangle in plane geometry, but also can be extended to the volume calculation of tetrahedron in three-dimensional space and other broader mathematical problems. In addition, using mathematical knowledge such as Helen's formula, we can solve some complicated problems, such as the maximum area and the shortest side of a triangle.

For some special types of triangles, such as equilateral triangles or isosceles right-angled triangles, a simpler formula can be used to calculate the area. For example, the area of an equilateral triangle is the square of its side length multiplied by the constant1/3; The area of an isosceles right triangle is the square of the length of its hypotenuse multiplied by the constant 1/2.