Point D is the midpoint of median AM of triangle ABC. Point E is the midpoint of AB, and point T is the intersection of BD and ME. Find the area of triangle DMT if [ABC] =180.

Answer 1

Let x = the length of AM.

The area of triangle ABC = (1/2)x^2

The area of triangle DMT = (1/2)(x/2)^2 = (1/8)x^2

Therefore, the area of triangle DMT = (1/8)[ABC] = (1/8)(180) = 22.5