TITLE: Corners are cut off from an equilateral triangle to produce a regular hexagon. Are the sides trisected?
QUESTION [8 upvotes]: The corners are cut off from an equilateral triangle to produce a regular hexagon. Are the sides of the triangle trisected?

In the actual question, the first line was exactly the same. It was then asked to find the ratio of area of the resulting hexagon and the original triangle. In the several solutions of this problem which I found on the internet, they had started with taking the sides of triangle as trisected by this operation and hence the side length of the hexagon would also be equal to one-third of the side length of triangle.
I have seen some variations of this problem where they had explicitly mentioned that the side was trisected and then hexagon was formed.
On stackexchange, there are problems in which they started by trisecting the sides (they mentioned it in the title) and getting a regular polygon.
My question is, if we cut off corners from the equilateral triangle to form regular hexagon, is it going to trisect the sides of triangle or not?

REPLY [2 votes]: In order to handle this question, be it about the size of the segments or the surface, don't look to this question as "cutting the edges of the equilateral triangle", but as "folding the edges of the equilateral triangle towards the centre": it produces exactly the same result (the equidistant hexagon), but the questions about segment length and surface become trivial.