I'm trying to remember where a maths problem came from that someone posted her a couple of years ago. I think it was from one of the maths competitions (probably intermediate), but although I've looked through them, I can't seem to see it.
It was a complex shape (hexagon/star like i think) made up of triangles of different colours. You were given an area of a small triangle and its base, I think. The question was about the area of a large triangle (or perhaps the area of the whole complex shape, which could be derived from the area of a large triangle).
It could be done with a brute force method of algebra and pythagoras, working out the height of one of the triangles and then using that in some way to find the overall sizes; it was complicated and ended up with fourth roots of things - but it did work.
And then there was the much more elegant way of solving it, which relied on the triangles being mathematically similar, probably equilateral (and you could tell the scale factor from the geometry of it), and then the area of the large one being proportional to the square of the scale factor.
It was a nice problem because it was possible - but very slow and needing quite a lot of determination! - to do it by the algebraic method, which perhaps seemed more obvious to students who are usually 'good' at maths, and yet so much nicer when you saw the other method. And I'd like to show someone again - but can't find it on the internet. I know it's there! I know we discussed it here and went over the various methods. But I just keep missing it when I look for it somehow. I could make up something similar, but it is never quite as good...
anyone remember it? Still have the link somewhere? thanks.