The meaning of each letter: S is the area, A is the base of the triangle, and H is the height of the triangle.

Deduction process:

1. Transform two congruent acute triangles into parallelograms:

This is a common method to find the triangle area. First, two congruent acute triangles are cut out, and the two triangles form a parallelogram one after another. Then compare and deduce.

After transforming into a parallelogram, it can be observed that the base of the parallelogram is the same as that of the triangle, and the height of the parallelogram is the same as that of the triangle. Since the parallelogram is composed of two congruent triangles, the area of the parallelogram is equal to that of the two triangles. From this, the formula can be deduced:

Two congruent acute triangles can also be transformed into rectangles for deduction.

As can be seen from the figure, the length and width of the rectangle correspond to the base and height of the triangle, and the area of the rectangle is equivalent to the area of two congruent triangles. Its formula derivation is the same as (1).

Source: Master of Mathematics Preparation