The median BM is drawn in triangles ABC with an area of 72 cm2. Find the area of triangle ABM.

Let’s build the height BH of the triangle ABC.

The area of the triangle ABC is equal to: Sавс = АС * ВН / 2 = 72 cm2.

The height BH is also the height of the ABM triangle, then the area of the ABM triangle is equal to:

Sawm = AM * BH / 2.

Since BM is the median of the triangle, then AM = CM = AC / 2.

Then, Sawm = (AC / 2) * BH / 2 = Savs / 2 = 72/2 = 36 cm2.

Answer: The area of the triangle ABM is 36 cm2.