How many triangles can be formed within a regular octagon, where vertices of the octagon are vertices of the triangles, and each triangle can have only one side common with that of the octagon, but n…

Question

How many triangles can be formed within a regular octagon, where vertices of the octagon are vertices of the triangles, and each triangle can have only one side common with that of the octagon, but none of the sides passes through the centre of the octagon?

PYQPulse · Accepted Answer

16

PYQPulse · Answer

Explanation: For each of the 8 sides, the third vertex must avoid the 2 adjacent vertices and the 2 vertices whose joining lines pass through the centre, leaving 2 valid vertices per side: 8 × 2 = 16 triangles.

How many triangles can be formed within a regular octagon, where vertices of the octagon are vertices of the triangles, and each triangle can have only one side common with that of the octagon, but none of the sides passes through the centre of the octagon?

Answer: B. 16

Explanation