Question
How many Triangles are there in the following figure?
✓
Answer
Every part A, B, C, D, E, F, G, H, I, J, K, L, M, N, O and P are 16 triangles.
Combining two at a time. A and $B , B$ and $C , C$ and $D , D$ and $A , J$ and $K , L$ and $M , N$ and $O , P$ and $I$ are 8 triangles.
Taking the combination of 4, we have I, J, E and $A, K, L, F$ and $B, M, N, G$ and $C, P, O, H$ and $D$ are 4 triangles.
Taking 8 parts together we have QRS, RST, STQ and TRQ are 4 triangles.
Total triangles $=16+8+4+4=32$ triangles.
Combining two at a time. A and $B , B$ and $C , C$ and $D , D$ and $A , J$ and $K , L$ and $M , N$ and $O , P$ and $I$ are 8 triangles.
Taking the combination of 4, we have I, J, E and $A, K, L, F$ and $B, M, N, G$ and $C, P, O, H$ and $D$ are 4 triangles.
Taking 8 parts together we have QRS, RST, STQ and TRQ are 4 triangles.
Total triangles $=16+8+4+4=32$ triangles.
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