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### Best Answer flysky says

Intuitively, the number must be even (because the shape is symmetric). I count 32 triangles: 8 yellow triangles, 2 small pale-yellow tringles*every of 8 outher vertex=16 and finally we have 8 big triangles (4+4).

Nice work.

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### Jason Link says

I count 32:

-8 small yellow triangles

-16 beige/yellow triangles (each beige figure makes 2: one with either small yellow triangle it touches)

-8 large triangles (2 beige/yellow triangles at either base, with a small yellow triangle at its point)

are we supposed to count the outer triangles (outside the figure) with only two sides each? In that case it would add 8 more triangles, totalling at 40.

### Moronke Odugbesan says

I counted the 8 pointed vertices and the 8 exterior triangles plus the 8 small yellow triangles=24 triangles + 8 triangles.Total is 32.

### jellohello says

Every triangle in the diagram has a yellow piece at one of the corners. For each yellow piece, there are four different triangles that contain that piece at a corner, with no triangles counted twice. Therefore the number is 8*4 = 32.