Question

How many triangles are there in the given figure?
(2 marks)

Answer 1

Every part A, B, C, D, E, F, G, H, I, J, K, L, M, N, O and P.
Number of triangles = 16

Combining two at a time. A & B, B & C, C & D, D & A, J & K, L & M, N & O, P & I
Number of triangles = 8
(0.5 marks)
Taking the combination of 4, we have I, J, E & A; K, L, F and B, M, N, G and C, P, O, H and D.
Number of triangles = 4
(0.5 marks)
Taking 8 parts together we have M, N, G, C, D, H, O & P; O, H, D, P, I, E, A & J, I, E, A, J, K, F, B, & L, and K, B, F, L, M, G, C & N.
Number of triangles = 4
(0.5 marks)
Total number of triangles = 16 + 8 + 4 + 4 = 32
(0.5 marks)