Inner Triangle
Maybe you've heard about the medians of a triangle... SPOILER! They meet in a single point. But what if instead of the median, you connected the vertices to a point a third of the way in between? A fifth?
You'd get a triangle. Is it similar to the original? What is its area?
Sketch inspired by the classic area problem at solvemymaths, http://solvemymaths.com/2015/04/13/area-problem-18/