Discussion
How many triangles are there in the given figure ?
(The figure is a rectangle divided by a vertical line into two squares, with both diagonals drawn in each square and a horizontal line drawn across the whole rectangle through the two points where the diagonals cross.)
Answer: D
There are 28 triangles in the figure.
Take each square as 2 units wide, so the whole figure is 4 by 2. Count by size:
| Triangle | Count |
|---|---|
| Smallest: halves of the left and right quarters of each square, cut by the horizontal line | 8 |
| Top and bottom quarters of each square | 4 |
| Whole left and right quarters of each square | 4 |
| Triangles across the middle line, on the horizontal line with apex at the top or bottom middle | 2 |
| Half-squares cut off by one diagonal | 8 |
| Large triangles with the whole long side as base and apex at the middle of the opposite side | 2 |
\[ 8 + 4 + 4 + 2 + 8 + 2 = 28 \]
Counting only the small pieces gives 12, and missing the triangles that span both squares gives 18 or less.
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