# Dissect a square-and-a-half into 4 equal pieces

The following shape is has the proportions of a square attached to a similar square divided diagonally - A square and a half, if you may.

The puzzle is to dissect the shape into 4 congruent pieces.

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

• Can the pieces be mirror images of each other? – user20 May 17 '14 at 17:52
• Yes, absolutely. But extra points if they aren't ;). – John Bupit May 17 '14 at 17:57
• they must be congruent then – ratchet freak May 17 '14 at 17:58
• Yes. I think it's more clear now. I was looking to avoid a mathematical term, though. – John Bupit May 17 '14 at 18:03
• For future reference, LiveGeometry is a wonderful tool. – user20 May 17 '14 at 18:15

## 2 Answers

The first thing to do is divide the figure into a number of sections which is a multiple of four. The easiest way to do this is to split it up into smaller triangles:

Note that there are now 12 sections, which divides into sections of 3. Three triangles forms a square and a smaller triangle. We know, as a result, that a square must go here (another way to do this is that the triangle in the corner must be part of a shape of three parts):

From this, it becomes clear where the rest of the divisions lie. The remaining triangle, as part of the triangular section, must be part of a set of three, so as a result, we know that it is as follows:

The rest of the divisions are simple:

And, as a side note, for future reference, LiveGeometry is a wonderful little tool.

• This one's way better than mine. – user88 May 17 '14 at 18:09
• @JoeZ. We have the same solution, though, to be fair! – user20 May 17 '14 at 18:11
• @John I won't choose for you, since that would be incredibly biased, but the canonical advice from Meta Stack Exchange on this topic is available in this FAQ answer under "Which answer should I choose?" – user20 May 17 '14 at 18:17
• @JohnBupit An answer with an explanation is always more useful than one with just the answer. (Not to say anything bad about Joe's answer; just in general.) That said, anyone can upvote either and your checkmark is yours to place :) – WendiKidd May 17 '14 at 21:42
• I would personally recommend you accept this answer (which you seem to have done, congrats). – user88 May 18 '14 at 15:05

The solution appears as follows:

It's a bit rough, but it shows the right places to cut the shape.