Polygon Complex

Geometry Level 2

If we want to exactly cover a regular octagon with triangles (of any kind), what is the least number of triangles that we must use?

3 4 5 6 7 8

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Lucien Gonnet
Oct 3, 2017

The sum of the angles of a n-sided polygon is (n-2)*180.

Therefore in an octagon we have 6*180 degrees to split between triangles.

We deduce that we need 6 triangle.

Wonseok Song
Jan 23, 2016

choose a vertex. draw lines to all other vertices. count triangles. no other method of decomposing into triangles works because any line from a vertex to a point on an edge will create a quadrilateral for the next polygon to be drawn.

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...