Discussion
Find the number of triangles in the following figure :
Answer: B
There are 22 triangles.
The two outer rectangles carry no diagonals and give none. The central block is two squares side by side, each with both diagonals drawn.
Each square gives 8: the 4 small triangles that meet at its centre, and the 4 half-square triangles cut off by its diagonals (two diagonals, two halves each). Two squares give 16. The two squares together give 2 more large triangles, one with its base along the whole top edge of the block and its apex at the middle of the bottom edge, and one the other way up. The small triangles standing on the top and bottom edges of the squares add 4 more, two above and two below.
The total is \(16 + 2 + 4 = 22\). Counting only 16 plus the 4 outer triangles gives 20, and 18 and 24 come from missing or double counting the large triangles.
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