Discussion
How many triangles are there in the given figure?
Answer: D
The figure holds 28 triangles.
Each of the three cells is a rectangle cut by both diagonals. Inside one cell there are 4 small triangles (the four parts the diagonals make) and 4 larger ones, each made of two small parts, with a side of the cell as the base. That is 8 per cell.
\[ 3 \times 8 = 24 \]
Triangles also span two neighbouring cells. Take the top edge of two adjacent cells as the base, with the apex at the bottom point where the diagonals meet on the shared line. The same works with the bottom edge and the apex at the top. That is 2 for each pair of neighbouring cells, and there are 2 such pairs.
\[ 24 + 2 \times 2 = 28 \]
No triangle spans all three cells, since the outer diagonals do not meet over a common apex.
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