Count Carefully! Numerous Triangles Ahead
Geometry
Level
2
How many triangles are there in the above figure?
The result will surprise you.
18
30
64
72
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Name the vertices along the base as A and B. Now count the possible number of possible triangles that always include point A as one the vertex. It comes out to be (4+3+2+1) 4=40. Now count the number of triangles that include vertex B and not include vertex A. This comes out to be (3+2+1) 4=24.
Note: No triangle can be formed without including either of the vertices A,B.
Hence total number of triangles = 40+24=64.