Divide a surface into equal sized areas

That's a no-brainer. I have very large match-sticks, so I can divide the triangle into two pieces of equal size with a single match-stick, using a variety of positions of the stick.

And if it can be done with one, it can be done with any number of match-sticks.

But I think that's not what you're after, and you implicitly assume some rules that you have not explained.

Luc

Assuming that only match-sticks with length 1 may be used, and they must be only inside the triangle, here is a solution for 2 match-sticks.

Luc

Here's a second solution using two match sticks:

An additional puzzle: Using four matchsticks divide the triangle area in three areas of equal size.

Good answers!

Both of you using Mathcad and it will be help for Machcad usage for the users. 

Match stick puzzle usually use unit length 1 and it put on dot points on the figure of the stick top or bottom.

Or the position can be fixed by using match sticks. 

If you got two and three stick answers, you can arrange them any number of this problem.

Then, using 12 all sticks in my picture and move two or more sticks to reduce the area size from 4*3/2=6 to 5, 4,3 and 2. I don't know the answer the area size is 1. Of course the minimum movement number of the sticks are the good answers.   

 Tokoro.

The one of 3D.