It is known that "there are two equal line segments parallel to the diagonal in a square to divide the square into three equal parts". Grasp the word "trisection", then the area of the triangle in the upper left corner is equal to the area of the middle part, equal to the area of the triangle in the lower right corner, and the areas of the three parts are equal. Then use 18.75÷3 to calculate the area of each part of the three equal parts, which is equal to 6.25.

Then grasp "there are two equal line segments parallel to the diagonal", because the diagonal divides the square into two isosceles right-angled triangles (the two sides are equal and the included angle between the two sides is right-angled), and the two line segments are parallel to the diagonal, so the triangle in the lower right corner and the triangle in the upper left corner are isosceles right-angled triangles. The area formula of isosceles right triangle is: multiply two right angles and divide by 2. If the triangle in the lower right corner is calculated, the area of the triangle in the lower right corner is 6.25.

Side length × side length ÷ 2 = 6.25

Side length × side length = 12.5

There is another formula: a property formula of triangle: in this problem, it is like this: the square of side length+the square of side length = the square of hypotenuse.

Namely: side length × side length+side length× side length = hypotenuse × hypotenuse.

When side length × side length = 12.5 is substituted, it is 12.5+ 12.5= hypotenuse × hypotenuse.

Then: hypotenuse × hypotenuse =25

Then, hypotenuse =5

Even if the required answer is obtained, the length of the required line segment is 5 cm.

The steps of direct writing are:

18.75÷3=6.25

Side length × side length ÷ 2 = 6.25

Side length × side length = 12.5

Side length × side length+side length× side length = hypotenuse × hypotenuse

12.5+ 12.5= hypotenuse × hypotenuse

Hypotenuse x hypotenuse = 25

Hypotenuse =5 (cm)