When you take one of the congruent right triangles with a h…

When you take one of the congruent right triangles with a hypotenuse of 6 cm (from the equilateral division) and treat this as the new base:
- Initially, this right triangle has a base of 3 cm and a hypotenuse of 6 cm, with the height from the original division of the equilateral triangle being \( 3\sqrt{3} \) cm.

Now, you're drawing a new perpendicular from the vertex to the hypotenuse (6 cm treated as the "new" base):
- By using the area concept of a triangle (Area \( = \frac{1}{2} \times \text{base} \times \text{height} \)), the area remains constant.