Question

How many triangles are there in each of the following figures?​
[4 Marks]

Answer 1

1) A, B, C, D, & E are five triangles.​

​No combination of these triangles taken 2 at a time, form any triangle.​ (0.5 Mark)

Only the combinations of​

A, F & C​

A, F & D​

B,F & E​

B, F & D ​

C, F & E ​ (1 Mark)

forms triangles when taken 3 triangles at a time. ​

Hence, the total number of triangles = 5 + 5 = 10. (0.5 Mark)

2) A, B, C, D, E, F, G, H are 8 triangles.​

Combination of these triangles taken 2 at a time, form 4 triangles ​

B, C​

D, E​

G, F​

H, A​ (0.5 Mark)

No combination of these triangles taken 3 at a time, form any triangle.​

Combination of these triangles taken 4 at a time, form 4 triangles. (0.5 Mark)

H, A, B & C​

B, C, D & E​

D, E, F & G​

F, G, H & A​ (0.5 Mark)

Hence, the total number of triangles = 8 + 4 + 4 = 16. (0.5 Mark)