How many triangles can be formed using the vertices of a regular dodecagon (a 12-sided polygon)?

Logic
Oct 18, 2018

#1**+2 **

For each side of the 12-gon, there are 12-4=8 non-adjacent vertices which you can use to form a triangle, so there are 12*8=96 such triangles. There are also those triangles which share two sides with the 12-gon, of which there are 12 (one for each vertex of the 12-gon--choose the two sides adjacent to the vertex). So there are 108 total excluded triangles, and thus the answer is (123)−108=220−108=112(123)−108=220−108=112.

Guest Oct 18, 2018