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### Best Answer CWanamaker says

There are 40 Triangles.

Each individual section has 5 small triangles. Since there are 4 sections this makes 20 triangles. Each section can also form a larger triangle with an adjacent sections. Since there are 4 combinations of adjacent sections that makes 4 x 5 = 20 as well.

So the answer is 5 x 4 for small triangle + 5x4 for the larger triangles = 40

I'm not sure if this is the shortcut way, but it was faster than counting all 40 of them.

### stanwshura says

There are 40 triangles: the "inner" or original 8 that are produced by twice diagonally bisesecting the smallest rectangle (or square, which is just an equilateral rectangle) from both sets of opposite corners, times the number of "rectangular layers" (including the innermost). I count 5. 5*8=40. Voi'la!

You got it.

### getitrite says

There are forty. I figured it out by looking at it head on, then looking at it with my head tilted to the right.

ha ha!