How Many Triangles in a Square?

The diagram shows a square cut into triangles. How many triangles of different suzes and types are there in the square?>br /> The are 16 small triangles.

There are 16 triangles, each formed from two smaller triangles. Inside each small square we can make a triangle from 2 triangles, then rotate it 4 times to get 4 x 4 =16 triangles.
Divide the large square ubti four along both diagonals to get 4 more triangles.
Divide the square into two along a diagonal, then this triangle can be rotated 4 times to give 4 triangles.
There are 16 + 16 + 4 + 4 = 44 triangles altogether.

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