Area of a triangle The following problem in elementary geometry was proposed to me. As a mathematical analyst, I confess that I can't solve it. And I have no idea of what I could do. Here it is: pick a triangle, and draw the three mediana (i.e. the segments that join a vertex with the midpoint of the opposite side). Use the three segments to construct a second triangle, and prove that the area of this triangle is $3/4$ times the area of the original triangle.
Any help is welcome.

Use vectors.It will be really helpful.Define sides of triangle ABC as A=0, B= b vector and C= c vector.
