What do you notice when you move the vertices of the larger triangle?

What is the area of the smaller triangle as a fraction of the larger triangle when each vertex of the larger triangle is connected to a point (1/3)rd of the way along the opposite edge?
(Try calculating for an equilateral triangle).
What is the area of the smaller triangle as a fraction of the larger triangle when each vertex of the larger triangle is connected to a point (1/n)th of the way along the opposite edge?
How could you extend this for (k/n)?