CONO-SUR 2013 Problem 6

Let $ABCD$ be a convex quadrilateral. Let $n \geq 2$ be a whole number. Prove that there are $n$ triangles with the same area that satisfy all of the following properties:

a) Their interiors are disjoint, that is, the triangles do not overlap. b) Each triangle lies either in $ABCD$ or inside of it. c) The sum of the areas of all of these triangles is at least $\frac{4n}{4n+1}$ the area of $ABCD$ .